QuestionFind the 8th term of the geometric sequence given by $a_{n}=6 \cdot(-2)^{(n-1)}$ . Options: A. -768 B. 768 C. -1536 D. 1536

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=6 \cdot(-)^{(n-1)}$ . We need to find the8th term of the sequence, i.e., $a_{8}$

STEP 2

To find the8th term of the sequence, we substitute $n=8$ into the explicit formula.
$a_{8}=6 \cdot(-2)^{(8-1)}$

STEP 3

implify the exponent in the formula.
$a_{8}=6 \cdot(-2)^{7}$

STEP 4

Calculate the value of $(-2)^{7}$ .
$(-2)^{7} = -128$

STEP 5

Substitute the calculated value back into the formula to find $a_{8}$ .
$a_{8}= \cdot(-128)$

STEP 6

Calculate the value of $a_{8}$ .
$a_{8}=6 \cdot(-128) = -768$ So, the8th term of the geometric sequence is -768.

Was this helpful?

QuestionFind the 8th term of the geometric sequence given by $a_{n}=6 \cdot(-2)^{(n-1)}$ . Options: A. -768 B. 768 C. -1536 D. 1536

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=6 \cdot(-)^{(n-1)}$ . We need to find the8th term of the sequence, i.e., $a_{8}$

STEP 2

To find the8th term of the sequence, we substitute $n=8$ into the explicit formula.
$a_{8}=6 \cdot(-2)^{(8-1)}$

STEP 3

implify the exponent in the formula.
$a_{8}=6 \cdot(-2)^{7}$

STEP 4

Calculate the value of $(-2)^{7}$ .
$(-2)^{7} = -128$

STEP 5

Substitute the calculated value back into the formula to find $a_{8}$ .
$a_{8}= \cdot(-128)$

STEP 6

Calculate the value of $a_{8}$ .
$a_{8}=6 \cdot(-128) = -768$ So, the8th term of the geometric sequence is -768.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the 8th term of the geometric sequence given by an=6⋅(−2)(n−1)a_{n}=6 \cdot(-2)^{(n-1)}an​=6⋅(−2)(n−1). Options: A. -768 B. 768 C. -1536 D. 1536

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by an=6⋅(−)(n−1)a_{n}=6 \cdot(-)^{(n-1)}an​=6⋅(−)(n−1) . We need to find the8th term of the sequence, i.e., a8a_{8}a8​

STEP 2

To find the8th term of the sequence, we substitute n=8n=8n=8 into the explicit formula.a8=6⋅(−2)(8−1)a_{8}=6 \cdot(-2)^{(8-1)}a8​=6⋅(−2)(8−1)

STEP 3

implify the exponent in the formula.a8=6⋅(−2)7a_{8}=6 \cdot(-2)^{7}a8​=6⋅(−2)7

STEP 4

Calculate the value of (−2)7(-2)^{7}(−2)7.(−2)7=−128(-2)^{7} = -128(−2)7=−128

STEP 5

Substitute the calculated value back into the formula to find a8a_{8}a8​.a8=⋅(−128)a_{8}= \cdot(-128)a8​=⋅(−128)

STEP 6

Calculate the value of a8a_{8}a8​.a8=6⋅(−128)=−768a_{8}=6 \cdot(-128) = -768a8​=6⋅(−128)=−768So, the8th term of the geometric sequence is -768.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the 8th term of the geometric sequence given by $a_{n}=6 \cdot(-2)^{(n-1)}$ . Options: A. -768 B. 768 C. -1536 D. 1536

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=6 \cdot(-)^{(n-1)}$ . We need to find the8th term of the sequence, i.e., $a_{8}$

To find the8th term of the sequence, we substitute $n=8$ into the explicit formula.
$a_{8}=6 \cdot(-2)^{(8-1)}$

implify the exponent in the formula.
$a_{8}=6 \cdot(-2)^{7}$

Calculate the value of $(-2)^{7}$ .
$(-2)^{7} = -128$

Substitute the calculated value back into the formula to find $a_{8}$ .
$a_{8}= \cdot(-128)$

Calculate the value of $a_{8}$ .
$a_{8}=6 \cdot(-128) = -768$ So, the8th term of the geometric sequence is -768.