QuestionFind the value of $a_{8}=(-1)^{8}(3 \cdot 8+5)$ . What is the result? Options: -27, 27, 29, -29.

Studdy Solution

STEP 1

Assumptions1. The formula given is $a_{n}=(-1)^{n}(3 n+5)$ . We are asked to substitute $n=8$ into the formula

STEP 2

Substitute $n=8$ into the formula.
$a_{8}=(-1)^{8}( \cdot8+5)$

STEP 3

Calculate the exponent of $-1$ .
$(-1)^{8}=1$ So, the formula becomes $a_{8}=1(3 \cdot8+5)$

STEP 4

Perform the multiplication inside the parentheses.
$3 \cdot8 =24$ So, the formula becomes $a_{8}=1(24+)$

STEP 5

Perform the addition inside the parentheses.
$24+5 =29$ So, the formula becomes $a_{8}=1 \cdot29$

STEP 6

Perform the multiplication.
$1 \cdot29 =29$ So, $a_{8}=29$ .
The result of substituting $8$ for $n$ in the formula $a_{n}=(-1)^{n}(3 n+5)$ is $29$ .

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QuestionFind the value of $a_{8}=(-1)^{8}(3 \cdot 8+5)$ . What is the result? Options: -27, 27, 29, -29.

Studdy Solution

STEP 1

Assumptions1. The formula given is $a_{n}=(-1)^{n}(3 n+5)$ . We are asked to substitute $n=8$ into the formula

STEP 2

Substitute $n=8$ into the formula.
$a_{8}=(-1)^{8}( \cdot8+5)$

STEP 3

Calculate the exponent of $-1$ .
$(-1)^{8}=1$ So, the formula becomes $a_{8}=1(3 \cdot8+5)$

STEP 4

Perform the multiplication inside the parentheses.
$3 \cdot8 =24$ So, the formula becomes $a_{8}=1(24+)$

STEP 5

Perform the addition inside the parentheses.
$24+5 =29$ So, the formula becomes $a_{8}=1 \cdot29$

STEP 6

Perform the multiplication.
$1 \cdot29 =29$ So, $a_{8}=29$ .
The result of substituting $8$ for $n$ in the formula $a_{n}=(-1)^{n}(3 n+5)$ is $29$ .

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QuestionFind the value of a8=(−1)8(3⋅8+5)a_{8}=(-1)^{8}(3 \cdot 8+5)a8​=(−1)8(3⋅8+5). What is the result? Options: -27, 27, 29, -29.

Studdy Solution

STEP 1

Assumptions1. The formula given is an=(−1)n(3n+5)a_{n}=(-1)^{n}(3 n+5)an​=(−1)n(3n+5). We are asked to substitute n=8n=8n=8 into the formula

STEP 2

Substitute n=8n=8n=8 into the formula.a8=(−1)8(⋅8+5)a_{8}=(-1)^{8}( \cdot8+5)a8​=(−1)8(⋅8+5)

STEP 3

Calculate the exponent of −1-1−1.(−1)8=1(-1)^{8}=1(−1)8=1So, the formula becomesa8=1(3⋅8+5)a_{8}=1(3 \cdot8+5)a8​=1(3⋅8+5)

STEP 4

Perform the multiplication inside the parentheses.3⋅8=243 \cdot8 =243⋅8=24So, the formula becomesa8=1(24+)a_{8}=1(24+)a8​=1(24+)

STEP 5

Perform the addition inside the parentheses.24+5=2924+5 =2924+5=29So, the formula becomesa8=1⋅29a_{8}=1 \cdot29a8​=1⋅29

STEP 6

Perform the multiplication.1⋅29=291 \cdot29 =291⋅29=29So, a8=29a_{8}=29a8​=29.The result of substituting 888 for nnn in the formula an=(−1)n(3n+5)a_{n}=(-1)^{n}(3 n+5)an​=(−1)n(3n+5) is 292929.

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QuestionFind the value of $a_{8}=(-1)^{8}(3 \cdot 8+5)$ . What is the result? Options: -27, 27, 29, -29.

Assumptions1. The formula given is $a_{n}=(-1)^{n}(3 n+5)$ . We are asked to substitute $n=8$ into the formula

Substitute $n=8$ into the formula.
$a_{8}=(-1)^{8}( \cdot8+5)$

Calculate the exponent of $-1$ .
$(-1)^{8}=1$ So, the formula becomes $a_{8}=1(3 \cdot8+5)$

Perform the multiplication inside the parentheses.
$3 \cdot8 =24$ So, the formula becomes $a_{8}=1(24+)$

Perform the addition inside the parentheses.
$24+5 =29$ So, the formula becomes $a_{8}=1 \cdot29$

Perform the multiplication.
$1 \cdot29 =29$ So, $a_{8}=29$ .
The result of substituting $8$ for $n$ in the formula $a_{n}=(-1)^{n}(3 n+5)$ is $29$ .