Question

what is the ninth term of the geometric sequence? 4, 12, 36, 108, ... a. 324 b. 972 c. 8748 d. 26244

Explanation:

Step1: Identify $a_1$ and $r$

$a_1 = 4$, $r = \frac{12}{4} = 3$

Step2: Use geometric sequence formula

The formula for the $n$-th term is $a_n = a_1 r^{n-1}$

Step3: Substitute $n=9$

$a_9 = 4 \times 3^{9-1} = 4 \times 3^8$

Step4: Calculate $3^8$ and multiply

$3^8 = 6561$, so $a_9 = 4 \times 6561 = 26244$

Answer:

d. 26244