Sequence

Problem 501

e the first term is 9 and the third term is $\frac{1}{81}$ . (Why are there two possible answers?) Find the 4 th term in the geometric sequence where the first term is 6 and the 7 th term is $\frac{3}{32}$ .
For the geometric sequence $3, m, n, 192, \ldots$ , find the values for $m$ and $n$ . Find the value of $x$ such that the following sequence forms a geometric progression: $x-1,3 x+4,6 x+8$

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Problem 502

Use the arithmetic sequence formula to find the 38th number in the sequence: $3,6,9 \ldots$

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Problem 503

Question 28 (1 point) Does the following statement demonstrate inductive reasoning or deductive reasoning?
For the pattern 4, 13, 22, 31, 40, the next term is 49.

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Problem 504

Type the missing number in this sequer 1, 3, 9, 27, 81,

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Problem 505

Question 3 (1 point) Imagine you need $\$ 425$ to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $\$ 30$ fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?
Your Answer: $\square$ Answer

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Problem 506

What is the next term in the sequence: A1, B2, D4, G7, K11, P16?

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Problem 507

What is the next number in the sequence: 142,857; 285,714; 428,571; 571,428; 714,285?

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Problem 508

Explain the difference between a sequence and a series. A sequence is a function whose domain is the set of positive integers. A series is a summation of the terms of a sequence. A sequence is a summation whose domain is the set of positive integers. A series is a function of the terms of a sequence. A series is a summation whose domain is the set of positive integers. A sequence is a function of the terms of a series. A series is a function whose domain is the set of positive integers. A sequence is a summation of the terms of a series.

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Problem 509

$\text{Write a formula for the general term (the nth term) of the arithmetic sequence } 5, 2, -1, -4. \text{ Then use the formula for } a_n \text{ to find } a_{20}.$

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Problem 510

Доказательство. Мы воспользуемся леммой 2.1.10 в случае необходимости и тогда можем считать, что неравенства выполнены для всех $n \geq 0$ . (1) Имеем для каждого $n \geq 2$ $x_{n}=x_{1} \cdot \frac{x_{2}}{x_{1}} \cdot \frac{x_{3}}{x_{2}} \cdots \frac{x_{n-1}}{x_{n-2}} \cdot \frac{x_{n}}{x_{n-1}}$
по условию $\frac{x_{2}}{x_{1}}, \frac{x_{3}}{x_{2}}, \ldots, \frac{x_{n}}{x_{n-1}} \leq q<1$
тогда $x_{n}=x_{1} \cdot \frac{x_{2}}{x_{1}} \cdot \frac{x_{3}}{x_{2}} \cdots \frac{x_{n-1}}{x_{n-2}} \cdot \frac{x_{n}}{x_{n-1}} \leq x_{1} q^{n-1}$
С другой стороны, (см. пример 2.1.4) ряд ( $q^{n}$ ) сходится при $q<1$ , а тогда по предложению 2.1.8 ряд ( $x_{1} q^{n}$ ) тоже сходится. Наконец, по признаку 1 (Следствие 2.2.2) ряд $\left(x_{n}\right)$ сходится.

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Problem 511

DEPARTMENT: SCIENCE LABORATORY TITLE: MTH 101
The $n^{th}$ term of the sequence is given as $3 \cdot 2^{2n}$ . Obtain the first four term of Sequence.

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Problem 512

A finite sequence is shown. $\{-25,-22,-19, \ldots, 32\}$
Which sigma notation can be used to represent the series for the finite sequence? Help: Introduction to Sigma Notation (video). $\sum_{n=1}^{18}(3 n-28)$ $\sum_{n=1}^{20}(3 n-28)$ $\sum_{n=1}^{20}(-3 n-22)$ $\sum_{n=1}^{18}(-3 n-22)$

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Problem 513

เi. on 5 - Notes C. Q Line Guide Reset Answer
This question has multiple parts. Be sure to answer all the parts of this question.
Each figure is created using green hexagon tiles. PART A
Is the sequence describing the number of green hexagons used in each figure an arithmetic or geometric sequence? Explain.
Figure 1 Figure 2 Figure 3 Enter your response here

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Problem 514

In the first 5 days of starting a business, Manny made $\$ 110$ , lost $\$ 75$ , had another loss of $\$ 39$ , and then made gains of $\$ 82$ and $\$ 146$ . How much money did Manny's business make over the first week?

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Problem 515

\begin{align} \text{Following transactions of Shrijal traders are given:} \\ \text{2075-1-1, Started business with bank Rs 1,00,000.} \\ \text{2075-1-5, Purchase Furniture of Rs 20,000 and amount paid by cheque.} \\ \text{2075-1-15, Goods sold to Hari of Rs 8,000.} \\ \text{2075-1-18, Wages paid to Rita by cheque of Rs 5,000.} \\ \text{2075-1-22, Cheque received from Hari of Rs 5,500.} \\ \text{2075-1-23, Purchase goods of Rs 12,000 from Sita and 60\% paid through bank.} \\ \text{2075-1-30, Salary paid of Rs 10,000 by cheque and outstanding salary paid Rs 2,000.} \\ \text{Prepare a simple bank book.} \end{align}

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Problem 516

3. There are 10 speakers at a conference with 5 of them men and different orders can they speak in if: a) Carly, David, and Elisa must immediately follow one another in any order? [2] b) Ben must go immediately after Alyssa? [2] c) They must present in alternating genders? [2] d) Jason and Shawn cannot speak immediately one after the other. [2] e) After the speeches, how many ways can they sit at a circular table for dinner? [2]

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Problem 517

Find the missing number in the pattern $1, 4, 9, 16, 25$ . Describe these numbers.

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Problem 518

Find the explicit formula for the arithmetic sequence starting with $a_{1}=26$ and the terms $26,33,40,47,54,61,\ldots$ .

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Problem 519

Place the following in order of increasing $I E_{1}$ .
N F As A) $\mathrm{N}<\mathrm{As}<\mathrm{F}$ B) $\mathrm{As}<\mathrm{N}<\mathrm{F}$ C) $\mathrm{F}<\mathrm{N}<\mathrm{As}$ D) $\mathrm{F}<\mathrm{As}<\mathrm{N}$ E) As $<\mathrm{F}<\mathrm{N}$

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Problem 520

Question 1 (a) Kapil opened a recurring deposit account in a bank. He deposits ₹ 1500 every month [3] for 2 years at $5 \%$ simple interest per annum. Find the total interest earned by Kapil on maturity. b) If $A=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}1 & 4 \\ 2 & 3\end{array}\right]$ and $C=\left[\begin{array}{ll}-1 & 2 \\ -2 & 5\end{array}\right]$ , find $A(B-C)$ . [3]
The table below shows the daily expenditure on food of 50 house-holds in a locality. [4] \begin{tabular}{|c|c|c|c|c|c|c|} \hline \begin{tabular}{c} Daily \\ Expenditure \\ (in ₹) \end{tabular} & $0-100$ & $100-200$ & $200-300$ & $300-400$ & $400-500$ & $500-600$ \\ \hline \begin{tabular}{c} Number of \\ House-holds \end{tabular} & 5 & 8 & 15 & 10 & 7 & 5 \\ \hline \end{tabular}
Using graph paper, draw a histogram representing the above distribution and estimate the mode. Take along $x$ -axis $2 \mathrm{~cm}=₹ 100$ and along $y$ -axis $2 \mathrm{~cm}=2$ Households.
This paper consists of 8 printed pages. 11 Turn Ov yright reserved.

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Problem 521

Вариант 48 Задача 1 Случайые $X_{1}, \ldots, X_{2 n}$ независимы. Также известио, что М $X_{i}=(-1)^{n}, \mathrm{D} X_{1}=2^{-1}, i \in\{1 \ldots \ldots, 2 n\}$ . Положим $S_{n}=\sum_{n-1}^{2 n} X_{n}$ . С помошью неравенства Чебышёва оценить веролтности $\mathrm{P}\left(\left|S_{n}\right| \geqslant 2 \sqrt{1-4^{-n}}\right)$ и $\mathrm{P}\left(\left|S_{n}\right|<2 \sqrt{1-4^{-n}}\right)$ .

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Problem 522

Given two terms in an arithmetic sequence find the recursive formula. 27) $a_{18}=3362$ and $a_{38}=7362$ 28) $a_{18}=44.3$ and $a_{33}=84.8$

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Problem 523

Find the arithmetic sequence for $a_{n}=5n+6$ starting with $n=1$ .

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Problem 524

Find the arithmetic sequence for $n=19$ given the formula $a_{n}=6n+0$ .

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Problem 525

Find the $11^{\text {th }}$ term of the sequence defined by $2 n^{2}-3$ .

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Problem 526

Find the first negative term $t$ and an expression for the $n^{\text{th}}$ term of the sequence: 32, 26, 20, 14, 8.

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Problem 527

Write an equation to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n=1$ for the first term. $34,-102,306, \ldots$
Write your answer using decimals and integers. $a_{n}=\square(\square)^{n-1}$ Submit

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Problem 528

Find the right number that fits the sequence. $\begin{array}{lllllll}7 & 4 & 10 & 12 & 13 & 36 & ?\end{array}$
49 25 16 15 72 Continue

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Problem 529

How many passes are expected to be executed to sort the maximum value using bubble sort algorithm in an array with $\mathrm{n}>1$ where n is the number of elements? 3 1 5 2 4 0

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Problem 530

Question: Convergence in Probability Let $X_{1}, X_{2}, \ldots$ be a sequence of independent and identically distributed (i.i.d.) random variables, where each $X_{i}$ has the following probability distribution: $P\left(X_{i}=0\right)=\frac{1}{2}, \quad P\left(X_{i}=1\right)=\frac{1}{2} .$ 1
Define the sample mean $\bar{X}_{n}$ as: $\bar{X}_{n}=\frac{1}{n} \sum_{i=1}^{n} X_{i} .$
We want to analyze the behavior of $\bar{X}_{n}$ as $n \rightarrow \infty$ . (a) Show that $E\left[X_{i}\right]=\frac{1}{2}$ and $\operatorname{Var}\left(X_{i}\right)=\frac{1}{4}$ . (b) Using the weak law of large numbers (WLLN), show that $\bar{X}_{n} \xrightarrow{P} \frac{1}{2}$ as $n \rightarrow \infty$ . That is, prove that $\bar{X}_{n}$ converges to $\frac{1}{2}$ in probability. (c) For a sequence $Y_{1}, Y_{2}, \ldots$ of independent random variables where $P\left(Y_{i}=\right.$ 1) $=1-\frac{1}{i}$ and $P\left(Y_{i}=0\right)=\frac{1}{i}$ , determine whether $Y_{n}$ converges in probability to 1 as $n \rightarrow \infty$ . Justify your answer using the definition of convergence in probability.

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Problem 531

Soit le sinte $\mu_{n}$ sefin por $\left\{\begin{array}{l}\mu_{0}=4 \\ \mu_{n+1}=\frac{1}{2}\end{array} \mu_{n}+5\right.$ a) calculer $\mu_{1}, \mu_{2}, \mu_{3}$ . b) justifier que (un) ni erthimethique ni Gcométrique o) expore $v_{n}=\mu_{n}-10$ . a) Montre que $\left(v_{n}\right)(S \cdot G)$ . b) Exprimer $v_{n}$ puis $u_{n}$ enfonction den d) oxpose $S_{n}=\sum_{k=0}^{n-1} v_{k}$ et $S_{n}^{\prime}=\sum_{k=0}^{n-1} \mu_{k}$ a) experime $S_{n}$ pins sn'enfonction dek. b) aluiler $S_{325}$ et $S_{2024}$ .

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Problem 532

Write an expression to describe the sequence below. Use $n$ to represent the position of a term Questions answered in the sequence, where $n=1$ for the first term. $-65,-64,-63,-62, \ldots$ 13

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Problem 533

Select the correct answer from each drop-down menu.
When she was 20, Liz started saving $\$ 6,000$ a year for retirement. Her goal is to reach $\$ 100,000$ in savings by the time she's 30 . Her account earns $8 \%$ interest per year, compounded annually. Liz $\square$ have saved $\$ 100,000$ by age 30 . She'll $\square$ her goal by about $\square$ Reset Next

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Problem 534

Identify the sequence type for $5, -4$ and find the next three terms if possible.

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Problem 535

Identify the sequence $100, 20, 4, \ldots$ as arithmetic, geometric, or neither.

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Problem 536

Identify the sequence type: $2, 4, 16, \ldots$ - is it arithmetic, geometric, or neither?

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Problem 537

Identify the sequence type: $10, 20, 30, \ldots$ - is it arithmetic, geometric, or neither?

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Problem 538

Determine if the sequence $200, 40, 8, \ldots$ is arithmetic, geometric, or neither.

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Problem 539

Identify the sequence: $6, 12, 18, \ldots$ as arithmetic, geometric, or neither.

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Problem 540

Determine if the sequence defined by $f(1)=10, f(n)=f(n-1)-1.5$ for $n \geq 2$ is arithmetic, geometric, or neither.

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Problem 541

Determine if the sequence $25, 5, 1, \ldots$ is arithmetic, geometric, or neither. How to modify one number to make it arithmetic or geometric?

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Problem 542

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

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Problem 543

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

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Problem 544

Identify the sequence type: 4, 9, 16, ... Is it Arithmetic, Geometric, or Neither?

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Problem 545

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

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Problem 546

1. Studiare la monotonia e determinare estremo inferiore e superiore della successione $a_{n}=\frac{\cos (n \pi)+n}{n^{2}+\arctan (n)} \quad \text { per } n \in \mathbb{N} \backslash\{0\}$ specificando se sono minimo e massimo.

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Problem 547

20. What is the fourth term in the expansion of $(a+b)^{4}$ ? a. $4 a^{3} b$ b. $a^{4}$ c. $6 a^{2} b^{2}$ d. $4 a b^{3}$

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Problem 548

The terms of the increasing arithmetic sequence $a_{n}$ are positive. The terms of the increasing geometric sequence $g_{n}$ are positive. The values of the first terms of both sequences are the same, and the values of the fourth terms of both sequences are the same. Which of the following statements describes the values of the second terms of the sequences?
A The second term of the arithmetic sequence must be less than the second term of the geometric sequence.
B The second term of the arithmetic sequence must be greater than the second term of the geometric sequence. (C) The second term of the arithmetic sequence must be the same value as the second term of the geometric sequence. (D) The relationship between the values of the second terms cannot be determined from the given information.

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Problem 549

A bell rings every 2 min and lights flash every 3 min. When did both occur together after the store opened at 1:00?

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Problem 550

Find the times when a bell rings every 2 min and lights flash every $3 \mathrm{~min}$ after the store opens at $10:00$ .

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Problem 551

Describe how to generate the next terms in the pattern: A: $5, 8, 11, 14, 17, \ldots$

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Problem 552

Identify the rule for generating terms in these sequences: a. Pattern A: 5, 8, 11, 14, 17, ... b. Pattern B: $\frac{1}{2}, 1, 2, 4, 8, ...$

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Problem 553

6. Assume a business is deciding whether to invest in a new project that is projected to generate profits of $\$ 90,000$ each year for the next three years. The project start-up costs are $\$ 225,000$ . (A) If the business normally earns 11 percent on its investments, should the business invest? Show/explain. (B) If the business normally earns 5 percent on its investments, should the business invest? Show/explain.

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Problem 554

A formula for the sequence $a_{n}: 2,14,98,686, \cdots$ , where $n \geq 0$ is
Select one: $7 \cdot 2^{n}$ $2+7 n$ $2 \cdot 7^{n}$ $7+2^{n}$

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Problem 555

Find arrangements of 5 letters from 'LANGSIR' starting with a vowel.

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Problem 556

The data shows the percentage of households (in decimals) using video streaming services from 2018 to 2022 in Canada. \begin{tabular}{|l|c|c|c|c|c|} \hline Year & 2018 & 2019 & 2020 & 2021 & 2022 \\ \hline \% of Households & 25 & 38 & 47 & 55 & 65 \\ \hline \end{tabular}
Estimate the instantaneous rate of change in the percent of households using video streaming services in the year 2019, using the averaging a preceding and following interval method.
ANSWER INSTRUCTIONS: - your answer should be rounded to the nearest tenth: - do no add extra spaces - do not add a unit of measurement

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Problem 557

```latex \text{Write the F Major Scale Ascending in the Bass Clef.} ```

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Problem 558

$\text { [6 } 3348663186 \text { 8] }$
How many comparisons will be performed in this array using sequential search for the searchltem 6? 7 2 1 4 3 6 5 0

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Problem 559

The input voltage $\mathrm{X}_{(t)}$ ), and output voltage $\mathrm{Y}_{(t)}$ of an electrical system are sampled simultaneously at regular intervals with the following results. $\begin{array}{r} n=0,1,2, \quad 3, \quad 4,5,6,7,8,9, \ldots \\ X(n T)=15,10,6,2, \quad 1,0,0,0,0,0, \ldots \\ Y(n T)=15,15,7.5,-2.75,-2.5, \cdots, \cdots,-,-\ldots \end{array}$
Calculate the missing values of the output voltage $\mathrm{Y}(\mathrm{nT})$ above. Mint: Assume that $\mathrm{X}(\mathrm{t})=0$ for $\mathrm{t}<0$ , and that only nonzero imputse response samples are $\mathrm{h}(\mathrm{n})$ , for $0 \leq \mathrm{n} \leq 4$ .

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Problem 560

8.1 .00 9.1 .00 10.1 .00 11.1 .00 12.1 .00 13.1 .00 14.1 .00

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Problem 561

Exercice 4 Soit la suite $\left(U_{n}\right)$ définiepar $\left\{\begin{array}{c}U_{0}=\frac{2}{3} \\ U_{n+1}=\frac{1}{2} U_{n}+\frac{n}{2 \sqrt{2}}+\frac{1}{\sqrt{2}}\end{array}\right.$
1. Calculer $U_{1}, U_{2}$ et $U_{3}$
2. On pose: $\forall n \geq 0 \quad V_{n}=U_{n} \sqrt{2}-n$ . a. Calculer $V_{0}, V_{1}$ et $V_{2}$ b. Montrer que $\left(V_{n}\right)$ est une suite géométrique c. Exprimer $\boldsymbol{V}_{\boldsymbol{n}}$ puis $\boldsymbol{U}_{\boldsymbol{n}}$ en fonction de $\boldsymbol{n}$ d. Calculer en fonction de $n: S_{n}=\sum_{k=0}^{k=n} v_{k}$

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Problem 562

Problem A Continue the two sequences of numbers below and find an equation to calculate the $n$ -th value: \begin{tabular}{c|c|c|c|c|c|c|c|c} $\mathbf{n}$ & $\mathbf{1}$ & $\mathbf{2}$ & $\mathbf{3}$ & $\mathbf{4}$ & $\mathbf{5}$ & $\mathbf{6}$ & $\mathbf{7}$ & Equation \\ \hline $a_{n}$ & 2 & 5 & 10 & 17 & 26 & 37 & & \\ \hline $b_{n}$ & 1 & 2 & 8 & 48 & 384 & 3840 & & \end{tabular}

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Problem 563

A new car is worth $\$ 25,000$ . However, it loses $12 \%$ of its value each year due to depreciation. Write an explicit formula describing the value of the car, $a_{n}$ , after $n$ years.

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Problem 564

12. Here are two sequencen: 1 EXAM
Sequence B a. For sequence $A$ , describe a way to produce each new term from the previous term. take Lle previas term and limes it by 10 b. For sequence B, describe a way to produce each new term from the previous term. c. Write a definition for the $n$ th term of sequence $A$ d. Write a definition for the nth term of sequence B e. If these sequences continue, then which is greater, $A(6)$ or $B(6)$ ? Explain or show how you know.

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Problem 565

A ball dropped from 256 feet bounces up $\frac{1}{4}$ of its fall height. What height on the third bounce?

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Problem 566

Find the next two numbers in the sequence: $1, 1 \frac{3}{4}, 2 \frac{1}{2}, 3 \frac{1}{4}$ .

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Problem 567

Next two numbers in the sequence: $7.5, 8.75, 10, 11.25$ . What are they?

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Problem 568

$\begin{array}{l}\text { rem Complete the pattern: } \\ \begin{array}{l} 4 \times \square \\ 4 \times=4 \\ 4 \times \\ 4 \times=400 \\ 4 \times \\ 4 \times=4,000 \\ 4 \times=40,000 \\ 4 \times=400,000 \\ 4\end{array}\end{array}$

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Problem 569

2) Theresa adds $\$ 3,000$ to her savings account on the first day of each year. Marcus adds $\$ 3,000$ to his savings account on the last day of each year. They both earn 7.5 percent annual interest. What is the difference in their savings account balances at the end of 34 years? You estimate that you will owe \$48,200 in student loans by the time you graduate. The interest rate is 6.52 percent. If you want to have this debt paid in full within six years, how much must you pay each month?

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Problem 570

Exercice ( 5 pts ) On considère la suite $U$ définie par $\left\{\begin{array}{c}U_{0}=\frac{2}{3} \\ U_{n+1}=\frac{3 U_{n}+2}{2 U_{n}+3} ; \forall n \in I N\end{array}\right.$
1. Calculer $\boldsymbol{U}_{\mathbf{1}} ; \boldsymbol{U}_{\mathbf{2}}$
2. Monter que $\forall n \in I N$ on a : $0 \leq U_{n} \leq 1$
3. On pose $V_{n}=\frac{U_{n}-1^{N}}{U_{n}+1}$ a. Monter que la suite $\left(V_{n}\right)$ est une suite géométrique b. Calculer $\boldsymbol{V}_{\boldsymbol{n}}$ puis $\boldsymbol{U}_{\boldsymbol{n}}$ en fonction de $n$ c. Calculer $S_{n}=\sum_{k=0}^{n} V_{n}$ d. Calculer $\lim V_{n} ; \lim U_{n}$ et $\lim S_{n}$

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Problem 571

Soit $\left\{U_{n}\right\}$ et $\left(V_{n}\right)$ deux suites définies par: $U_{n}=\frac{2^{n}+4 n+3}{2}$ et $V_{n}=\frac{2^{n}-4 n+3}{2}$ On pose $T_{1}=U_{n}+V_{n}$ et $T_{2}=U_{n}-V_{n}$ 1) Montrer que $T_{1}$ est géométrique et que $T_{2}$ est arithmétique ? 2) En déduire $S_{1}$ et $S_{2}$ en fonction de $n$ tels que: $S_{1}=\sum_{K=0}^{n} \boldsymbol{U}_{K}$ et $S_{2}=\sum_{K=0}^{n} V_{K}$

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1 ...3 4 5 6

Sequence

Problem 501

Problem 502

Use the arithmetic sequence formula to find the 38th number in the sequence: 3,6,9…3,6,9 \ldots3,6,9…

Problem 503

Question 28 (1 point) Does the following statement demonstrate inductive reasoning or deductive reasoning?For the pattern 4, 13, 22, 31, 40, the next term is 49.

Problem 504

Type the missing number in this sequer 1, 3, 9, 27, 81,

Problem 505

Question 3 (1 point) Imagine you need $425\$ 425$425 to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $30\$ 30$30 fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?Your Answer: □\square□ Answer

Problem 506

What is the next term in the sequence: A1, B2, D4, G7, K11, P16?

Problem 507

What is the next number in the sequence: 142,857; 285,714; 428,571; 571,428; 714,285?

Problem 508

Problem 509

Problem 510

Problem 511

DEPARTMENT: SCIENCE LABORATORY TITLE: MTH 101The nthn^{th}nth term of the sequence is given as 3⋅22n3 \cdot 2^{2n}3⋅22n. Obtain the first four term of Sequence.

Problem 512

Problem 513

Problem 514

In the first 5 days of starting a business, Manny made $110\$ 110$110, lost $75\$ 75$75, had another loss of $39\$ 39$39, and then made gains of $82\$ 82$82 and $146\$ 146$146. How much money did Manny's business make over the first week?

Problem 515

Problem 516

Problem 517

Find the missing number in the pattern 1,4,9,16,251, 4, 9, 16, 251,4,9,16,25. Describe these numbers.

Problem 518

Find the explicit formula for the arithmetic sequence starting with a1=26a_{1}=26a1​=26 and the terms 26,33,40,47,54,61,…26,33,40,47,54,61,\ldots26,33,40,47,54,61,….

Problem 519

Place the following in order of increasing IE1I E_{1}IE1​.N F As A) N<As<F\mathrm{N}<\mathrm{As}<\mathrm{F}N<As<F B) As<N<F\mathrm{As}<\mathrm{N}<\mathrm{F}As<N<F C) F<N<As\mathrm{F}<\mathrm{N}<\mathrm{As}F<N<As D) F<As<N\mathrm{F}<\mathrm{As}<\mathrm{N}F<As<N E) As <F<N<\mathrm{F}<\mathrm{N}<F<N

Problem 520

Problem 521

Problem 522

Given two terms in an arithmetic sequence find the recursive formula. 27) a18=3362a_{18}=3362a18​=3362 and a38=7362a_{38}=7362a38​=7362 28) a18=44.3a_{18}=44.3a18​=44.3 and a33=84.8a_{33}=84.8a33​=84.8

Problem 523

Find the arithmetic sequence for an=5n+6a_{n}=5n+6an​=5n+6 starting with n=1n=1n=1.

Problem 524

Find the arithmetic sequence for n=19n=19n=19 given the formula an=6n+0a_{n}=6n+0an​=6n+0.

Problem 525

Find the 11th 11^{\text {th }}11th term of the sequence defined by 2n2−32 n^{2}-32n2−3.

Problem 526

Find the first negative term ttt and an expression for the nthn^{\text{th}}nth term of the sequence: 32, 26, 20, 14, 8.

Problem 527

Problem 528

Find the right number that fits the sequence. 7410121336?\begin{array}{lllllll}7 & 4 & 10 & 12 & 13 & 36 & ?\end{array}7​4​10​12​13​36​?​49 25 16 15 72 Continue

Problem 529

How many passes are expected to be executed to sort the maximum value using bubble sort algorithm in an array with n>1\mathrm{n}>1n>1 where n is the number of elements? 3 1 5 2 4 0

Problem 530

Problem 531

Problem 532

Write an expression to describe the sequence below. Use nnn to represent the position of a term Questions answered in the sequence, where n=1n=1n=1 for the first term. −65,−64,−63,−62,…-65,-64,-63,-62, \ldots−65,−64,−63,−62,… 13

Problem 533

Problem 534

Identify the sequence type for 5,−45, -45,−4 and find the next three terms if possible.

Problem 535

Identify the sequence 100,20,4,…100, 20, 4, \ldots100,20,4,… as arithmetic, geometric, or neither.

Problem 536

Identify the sequence type: 2,4,16,…2, 4, 16, \ldots2,4,16,… - is it arithmetic, geometric, or neither?

Problem 537

Identify the sequence type: 10,20,30,…10, 20, 30, \ldots10,20,30,… - is it arithmetic, geometric, or neither?

Problem 538

Determine if the sequence 200,40,8,…200, 40, 8, \ldots200,40,8,… is arithmetic, geometric, or neither.

Problem 539

Identify the sequence: 6,12,18,…6, 12, 18, \ldots6,12,18,… as arithmetic, geometric, or neither.

Problem 540

Determine if the sequence defined by f(1)=10,f(n)=f(n−1)−1.5f(1)=10, f(n)=f(n-1)-1.5f(1)=10,f(n)=f(n−1)−1.5 for n≥2n \geq 2n≥2 is arithmetic, geometric, or neither.

Problem 541

Determine if the sequence 25,5,1,…25, 5, 1, \ldots25,5,1,… is arithmetic, geometric, or neither. How to modify one number to make it arithmetic or geometric?

Problem 542

Match the recursive definition h(1)=1,h(n)=2∗h(n−1)+1h(1)=1, h(n)=2 * h(n-1)+1h(1)=1,h(n)=2∗h(n−1)+1 with the correct sequence: A. 80,40,20,10,580,40,20,10,580,40,20,10,5 B. 1,2,4,8,161,2,4,8,161,2,4,8,16 C. 1,3,7,15,311,3,7,15,311,3,7,15,31

Problem 543

Identify the sequence type: 25,19,13,…25, 19, 13, \ldots25,19,13,… Is it Arithmetic, Geometric, or Neither?

Problem 544

Identify the sequence type: 4, 9, 16, ... Is it Arithmetic, Geometric, or Neither?

Problem 545

Identify the sequence: 50,60,70,…50, 60, 70, \ldots50,60,70,…. Is it Arithmetic, Geometric, or Neither?

Problem 546

Problem 547

20. What is the fourth term in the expansion of (a+b)4(a+b)^{4}(a+b)4 ? a. 4a3b4 a^{3} b4a3b b. a4a^{4}a4 c. 6a2b26 a^{2} b^{2}6a2b2 d. 4ab34 a b^{3}4ab3

Use the arithmetic sequence formula to find the 38th number in the sequence: $3,6,9 \ldots$

Question 28 (1 point) Does the following statement demonstrate inductive reasoning or deductive reasoning?
For the pattern 4, 13, 22, 31, 40, the next term is 49.

Question 3 (1 point) Imagine you need $\$ 425$ to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $\$ 30$ fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?
Your Answer: $\square$ Answer

DEPARTMENT: SCIENCE LABORATORY TITLE: MTH 101
The $n^{th}$ term of the sequence is given as $3 \cdot 2^{2n}$ . Obtain the first four term of Sequence.

In the first 5 days of starting a business, Manny made $\$ 110$ , lost $\$ 75$ , had another loss of $\$ 39$ , and then made gains of $\$ 82$ and $\$ 146$ . How much money did Manny's business make over the first week?

Find the missing number in the pattern $1, 4, 9, 16, 25$ . Describe these numbers.

Find the explicit formula for the arithmetic sequence starting with $a_{1}=26$ and the terms $26,33,40,47,54,61,\ldots$ .

Place the following in order of increasing $I E_{1}$ .
N F As A) $\mathrm{N}<\mathrm{As}<\mathrm{F}$ B) $\mathrm{As}<\mathrm{N}<\mathrm{F}$ C) $\mathrm{F}<\mathrm{N}<\mathrm{As}$ D) $\mathrm{F}<\mathrm{As}<\mathrm{N}$ E) As $<\mathrm{F}<\mathrm{N}$

Given two terms in an arithmetic sequence find the recursive formula. 27) $a_{18}=3362$ and $a_{38}=7362$ 28) $a_{18}=44.3$ and $a_{33}=84.8$

Find the arithmetic sequence for $a_{n}=5n+6$ starting with $n=1$ .

Find the arithmetic sequence for $n=19$ given the formula $a_{n}=6n+0$ .

Find the $11^{\text {th }}$ term of the sequence defined by $2 n^{2}-3$ .

Find the first negative term $t$ and an expression for the $n^{\text{th}}$ term of the sequence: 32, 26, 20, 14, 8.

Find the right number that fits the sequence. $\begin{array}{lllllll}7 & 4 & 10 & 12 & 13 & 36 & ?\end{array}$
49 25 16 15 72 Continue

How many passes are expected to be executed to sort the maximum value using bubble sort algorithm in an array with $\mathrm{n}>1$ where n is the number of elements? 3 1 5 2 4 0

Write an expression to describe the sequence below. Use $n$ to represent the position of a term Questions answered in the sequence, where $n=1$ for the first term. $-65,-64,-63,-62, \ldots$ 13

Identify the sequence type for $5, -4$ and find the next three terms if possible.

Identify the sequence $100, 20, 4, \ldots$ as arithmetic, geometric, or neither.

Identify the sequence type: $2, 4, 16, \ldots$ - is it arithmetic, geometric, or neither?

Identify the sequence type: $10, 20, 30, \ldots$ - is it arithmetic, geometric, or neither?

Determine if the sequence $200, 40, 8, \ldots$ is arithmetic, geometric, or neither.

Identify the sequence: $6, 12, 18, \ldots$ as arithmetic, geometric, or neither.

Determine if the sequence defined by $f(1)=10, f(n)=f(n-1)-1.5$ for $n \geq 2$ is arithmetic, geometric, or neither.

Determine if the sequence $25, 5, 1, \ldots$ is arithmetic, geometric, or neither. How to modify one number to make it arithmetic or geometric?

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

20. What is the fourth term in the expansion of $(a+b)^{4}$ ? a. $4 a^{3} b$ b. $a^{4}$ c. $6 a^{2} b^{2}$ d. $4 a b^{3}$

Find the times when a bell rings every 2 min and lights flash every $3 \mathrm{~min}$ after the store opens at $10:00$ .

Describe how to generate the next terms in the pattern: A: $5, 8, 11, 14, 17, \ldots$

Identify the rule for generating terms in these sequences: a. Pattern A: 5, 8, 11, 14, 17, ... b. Pattern B: $\frac{1}{2}, 1, 2, 4, 8, ...$

A formula for the sequence $a_{n}: 2,14,98,686, \cdots$ , where $n \geq 0$ is
Select one: $7 \cdot 2^{n}$ $2+7 n$ $2 \cdot 7^{n}$ $7+2^{n}$

$\text { [6 } 3348663186 \text { 8] }$
How many comparisons will be performed in this array using sequential search for the searchltem 6? 7 2 1 4 3 6 5 0

A new car is worth $\$ 25,000$ . However, it loses $12 \%$ of its value each year due to depreciation. Write an explicit formula describing the value of the car, $a_{n}$ , after $n$ years.

A ball dropped from 256 feet bounces up $\frac{1}{4}$ of its fall height. What height on the third bounce?

Find the next two numbers in the sequence: $1, 1 \frac{3}{4}, 2 \frac{1}{2}, 3 \frac{1}{4}$ .

Next two numbers in the sequence: $7.5, 8.75, 10, 11.25$ . What are they?