Math  /  Algebra

QuestionY Score: 0/5 Penalty: none 2024/2025 School Year Home Announcements Assignments Modules Clever Log In DeltaMath Desmos calculator Question What is a formula for the nth term of the given sequence? 15, 21, 27... Answer Oan = 15-6(n − 1) © ɑn an = 21-6n an = 21+ 6(n - 1) an = 15+ 6(n - 1) ɑn Copyright ©2024 DeltaMath.com All Rights Reserved. Privacy Policy | Terms of Service

Studdy Solution

STEP 1

What is this asking? We need to find a formula that gives us the *n*th number in a sequence, where the first number is 15, the second is 21, and the third is 27, and so on. Watch out! It's easy to mess up the starting number and the amount we add each time, so double-check your formula with the first few numbers in the sequence!

STEP 2

1. Find the common difference.
2. Build the formula.
3. Check the formula.

STEP 3

Let's **find the common difference**, which is how much we add to get from one number to the next.
Going from 15 to 21, we add 15+x=2115 + x = 21, so x=2115=6x = 21 - 15 = 6.
Going from 21 to 27, we add 21+x=2721 + x = 27, so x=2721=6x = 27 - 21 = 6.
The **common difference** is 66!

STEP 4

The formula for the *n*th term of an arithmetic sequence is an=a1+d(n1)a_n = a_1 + d(n-1), where a1a_1 is the **first term** and *d* is the **common difference**.
This formula basically says: "Start at the first term and add the common difference a certain number of times."

STEP 5

In our case, the **first term** a1a_1 is 1515 and the **common difference** *d* is 66.
Plugging these values into the formula, we get an=15+6(n1)a_n = 15 + 6(n-1).

STEP 6

Let's **test it out**!
If n=1n=1, a1=15+6(11)=15+60=15a_1 = 15 + 6(1-1) = 15 + 6 \cdot 0 = 15.
Perfect! If n=2n=2, a2=15+6(21)=15+61=21a_2 = 15 + 6(2-1) = 15 + 6 \cdot 1 = 21.
Awesome! If n=3n=3, a3=15+6(31)=15+62=15+12=27a_3 = 15 + 6(3-1) = 15 + 6 \cdot 2 = 15 + 12 = 27.
It works!

STEP 7

The formula for the *n*th term of the sequence is an=15+6(n1)a_n = 15 + 6(n-1).

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