QuestionFind the general formula for the sequence $\{-1/2, 0, 1/2, 1, \ldots\}$ . Options: $a_n=(-1/2)n+1$ , $a_n=n+1/2$ , $a_n=(1/2)n-1$ , $a_n=n-1/2$ .

Studdy Solution

STEP 1

Assumptions1. The sequence given is $\{-1 /,0,1 /,1, \ldots\}$ . . We are looking for a general formula for the nth term of the sequence, denoted as $a_n$ .

STEP 2

Let's examine the sequence to understand its pattern. The sequence starts at -1/2 and increases by1/2 with each term.

STEP 3

Let's try to express this pattern in a general formula. The nth term of the sequence, $a_n$ , should be equal to the first term plus the difference times (n-1).
$a_n = a1 + (n-1) \times d$

STEP 4

In our sequence, the first term $a1$ is -1/2 and the difference $d$ is1/2.

STEP 5

Substitute the values of $a1$ and $d$ into the general formula.
$a_n = -1/2 + (n-1) \times1/2$

STEP 6

implify the equation.
$a_n = -1/2 + n/2 -1/2$

STEP 7

Combine like terms.
$a_n = n/2 -1$ So, the general formula for the sequence $\{-1 /2,0,1 /2,1, \ldots\}$ is $a_n = n/2 -1$ .

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QuestionFind the general formula for the sequence $\{-1/2, 0, 1/2, 1, \ldots\}$ . Options: $a_n=(-1/2)n+1$ , $a_n=n+1/2$ , $a_n=(1/2)n-1$ , $a_n=n-1/2$ .

Studdy Solution

STEP 1

Assumptions1. The sequence given is $\{-1 /,0,1 /,1, \ldots\}$ . . We are looking for a general formula for the nth term of the sequence, denoted as $a_n$ .

STEP 2

Let's examine the sequence to understand its pattern. The sequence starts at -1/2 and increases by1/2 with each term.

STEP 3

Let's try to express this pattern in a general formula. The nth term of the sequence, $a_n$ , should be equal to the first term plus the difference times (n-1).
$a_n = a1 + (n-1) \times d$

STEP 4

In our sequence, the first term $a1$ is -1/2 and the difference $d$ is1/2.

STEP 5

Substitute the values of $a1$ and $d$ into the general formula.
$a_n = -1/2 + (n-1) \times1/2$

STEP 6

implify the equation.
$a_n = -1/2 + n/2 -1/2$

STEP 7

Combine like terms.
$a_n = n/2 -1$ So, the general formula for the sequence $\{-1 /2,0,1 /2,1, \ldots\}$ is $a_n = n/2 -1$ .

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QuestionFind the general formula for the sequence {−1/2,0,1/2,1,…}\{-1/2, 0, 1/2, 1, \ldots\}{−1/2,0,1/2,1,…}. Options: an=(−1/2)n+1a_n=(-1/2)n+1an​=(−1/2)n+1, an=n+1/2a_n=n+1/2an​=n+1/2, an=(1/2)n−1a_n=(1/2)n-1an​=(1/2)n−1, an=n−1/2a_n=n-1/2an​=n−1/2.

Studdy Solution

STEP 1

Assumptions1. The sequence given is {−1/,0,1/,1,…}\{-1 /,0,1 /,1, \ldots\}{−1/,0,1/,1,…}. . We are looking for a general formula for the nth term of the sequence, denoted as ana_nan​.

STEP 2

Let's examine the sequence to understand its pattern. The sequence starts at -1/2 and increases by1/2 with each term.

STEP 3

Let's try to express this pattern in a general formula. The nth term of the sequence, ana_nan​, should be equal to the first term plus the difference times (n-1).an=a1+(n−1)×da_n = a1 + (n-1) \times dan​=a1+(n−1)×d

STEP 4

In our sequence, the first term a1a1a1 is -1/2 and the difference ddd is1/2.

STEP 5

Substitute the values of a1a1a1 and ddd into the general formula.an=−1/2+(n−1)×1/2a_n = -1/2 + (n-1) \times1/2an​=−1/2+(n−1)×1/2

STEP 6

implify the equation.an=−1/2+n/2−1/2a_n = -1/2 + n/2 -1/2an​=−1/2+n/2−1/2

STEP 7

Combine like terms.an=n/2−1a_n = n/2 -1an​=n/2−1So, the general formula for the sequence {−1/2,0,1/2,1,…}\{-1 /2,0,1 /2,1, \ldots\}{−1/2,0,1/2,1,…} is an=n/2−1a_n = n/2 -1an​=n/2−1.

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QuestionFind the general formula for the sequence $\{-1/2, 0, 1/2, 1, \ldots\}$ . Options: $a_n=(-1/2)n+1$ , $a_n=n+1/2$ , $a_n=(1/2)n-1$ , $a_n=n-1/2$ .

Assumptions1. The sequence given is $\{-1 /,0,1 /,1, \ldots\}$ . . We are looking for a general formula for the nth term of the sequence, denoted as $a_n$ .

Let's try to express this pattern in a general formula. The nth term of the sequence, $a_n$ , should be equal to the first term plus the difference times (n-1).
$a_n = a1 + (n-1) \times d$

In our sequence, the first term $a1$ is -1/2 and the difference $d$ is1/2.

Substitute the values of $a1$ and $d$ into the general formula.
$a_n = -1/2 + (n-1) \times1/2$

implify the equation.
$a_n = -1/2 + n/2 -1/2$

Combine like terms.
$a_n = n/2 -1$ So, the general formula for the sequence $\{-1 /2,0,1 /2,1, \ldots\}$ is $a_n = n/2 -1$ .