question\nfind the 9th term of the geometric sequence 6, 24, 96, ...

Explanation:

Step1: Find the common ratio

The common ratio $r$ of a geometric - sequence is found by dividing a term by its previous term. For the sequence $6,24,96,\cdots$, $r=\frac{24}{6}=4$.

Step2: Recall the formula for the $n$th term of a geometric sequence

The formula for the $n$th term of a geometric sequence is $a_n=a_1r^{n - 1}$, where $a_1$ is the first - term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 6$, $r = 4$, and $n=9$.

Step3: Substitute the values into the formula

Substitute $a_1 = 6$, $r = 4$, and $n = 9$ into the formula $a_n=a_1r^{n - 1}$. We get $a_9=6\times4^{9 - 1}=6\times4^8$.

Step4: Calculate $4^8$

$4^8=(2^2)^8=2^{16}$. $4^8 = 65536$.

Step5: Calculate $a_9$

$a_9=6\times65536 = 393216$.

Answer:

$393216$