Find a formula for the nth term of the following geometric sequence, then find the 4th 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 common ratio can be found by dividing any term by the previous term. For example, $$\frac{144}{36}=4$$
So the common ratio is 4.
To find the formula for the nth term, we use the formula for a geometric sequence:
$$a_n=a_1 \cdot r^{n-1}$$
where $a_1$ is the first term and $r$ is the common ratio.
In this case, $a_1=9$ and $r=4$, so:
$$a_n=9 \cdot 4^{n-1}$$
To find the 4th term, we simply substitute $n=4$ into the formula:
$$a_4=9 \cdot 4^{4-1}=9 \cdot 4^3=9 \cdot 64=576$$
So the answer is D.

Find a Formula for the Nth Term of the Following 9,36,144,…9,36,144 , \ldots9,36,144,…

Find a Formula for the Nth Term of the Following $9,36,144 , \ldots$