Question

find the 9th term of the geometric sequence 9, 27, 81, ...

Explanation:

Step1: Find the common ratio

The common ratio $r$ of a geometric sequence is found by dividing a term by its previous term. So, $r=\frac{27}{9}=3$.

Step2: Identify the first - term and the formula

The first - term $a_1 = 9$, and the formula for the $n$th term of a geometric sequence is $a_n=a_1r^{n - 1}$.

Step3: Calculate the 9th term

Substitute $a_1 = 9$, $r = 3$, and $n = 9$ into the formula: $a_9=9\times3^{9 - 1}=9\times3^8$. Since $3^8=6561$, then $a_9=9\times6561 = 59049$.

Answer:

$59049$