QuestionFind the 7th term in the sequence given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . Options: A. 6561 B. -6561 C. -2187 D. 2187

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . We are asked to find the7th term in the sequence, i.e., $a_{7}$

STEP 2

To find the7th term in the sequence, we substitute $n=7$ into the explicit formula.
$a_{7}=- \cdot()^{(7-1)}$

STEP 3

implify the exponent in the formula.
$a_{7}=-3 \cdot(3)^{6}$

STEP 4

Calculate the value of $3^{6}$ .
$3^{6} =729$ So, the formula becomes $a_{7}=-3 \cdot729$

STEP 5

Finally, calculate the7th term in the sequence.
$a_{7}=-3 \cdot729 = -2187$ So, the7th term in the sequence is -2187.The correct answer is C. -2187.

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QuestionFind the 7th term in the sequence given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . Options: A. 6561 B. -6561 C. -2187 D. 2187

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . We are asked to find the7th term in the sequence, i.e., $a_{7}$

STEP 2

To find the7th term in the sequence, we substitute $n=7$ into the explicit formula.
$a_{7}=- \cdot()^{(7-1)}$

STEP 3

implify the exponent in the formula.
$a_{7}=-3 \cdot(3)^{6}$

STEP 4

Calculate the value of $3^{6}$ .
$3^{6} =729$ So, the formula becomes $a_{7}=-3 \cdot729$

STEP 5

Finally, calculate the7th term in the sequence.
$a_{7}=-3 \cdot729 = -2187$ So, the7th term in the sequence is -2187.The correct answer is C. -2187.

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QuestionFind the 7th term in the sequence given by an=−3⋅(3)(n−1)a_{n}=-3 \cdot(3)^{(n-1)}an​=−3⋅(3)(n−1). Options: A. 6561 B. -6561 C. -2187 D. 2187

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the geometric sequence is given by an=−3⋅(3)(n−1)a_{n}=-3 \cdot(3)^{(n-1)}an​=−3⋅(3)(n−1) . We are asked to find the7th term in the sequence, i.e., a7a_{7}a7​

STEP 2

To find the7th term in the sequence, we substitute n=7n=7n=7 into the explicit formula.a7=−⋅()(7−1)a_{7}=- \cdot()^{(7-1)}a7​=−⋅()(7−1)

STEP 3

implify the exponent in the formula.a7=−3⋅(3)6a_{7}=-3 \cdot(3)^{6}a7​=−3⋅(3)6

STEP 4

Calculate the value of 363^{6}36.36=7293^{6} =72936=729So, the formula becomesa7=−3⋅729a_{7}=-3 \cdot729a7​=−3⋅729

STEP 5

Finally, calculate the7th term in the sequence.a7=−3⋅729=−2187a_{7}=-3 \cdot729 = -2187a7​=−3⋅729=−2187So, the7th term in the sequence is -2187.The correct answer is C. -2187.

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

QuestionFind the 7th term in the sequence given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . Options: A. 6561 B. -6561 C. -2187 D. 2187

Assumptions1. The explicit formula for the geometric sequence is given by $a_{n}=-3 \cdot(3)^{(n-1)}$ . We are asked to find the7th term in the sequence, i.e., $a_{7}$

To find the7th term in the sequence, we substitute $n=7$ into the explicit formula.
$a_{7}=- \cdot()^{(7-1)}$

implify the exponent in the formula.
$a_{7}=-3 \cdot(3)^{6}$

Calculate the value of $3^{6}$ .
$3^{6} =729$ So, the formula becomes $a_{7}=-3 \cdot729$

Finally, calculate the7th term in the sequence.
$a_{7}=-3 \cdot729 = -2187$ So, the7th term in the sequence is -2187.The correct answer is C. -2187.