Find a formula for the $n t h$ term of the following geometric sequence, then find the 4 th term of the sequence.
$9,36,144 , \ldots$
A) $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 576$
B) $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 2304$
C) $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 2304$
D) $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 576$
E) $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 144$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with a common ratio of 4 (each term is 4 times the previous term). The first term $a_1 = 9$, so the $n$th term formula is $a_n = 9 \cdot 4^{n-1}$. For the 4th term, $a_4 = 9 \cdot 4^{4-1} = 9 \cdot 4^3 = 9 \cdot 64 = 576$.

Find a Formula for The nthn t hnth Term of the Following Geometric Sequence, Then Find the 4

Find a Formula for The $n t h$ Term of the Following Geometric Sequence, Then Find the 4