Question

value: 3
what is the ninth term of the geometric sequence?
8, -16, 32, -64, ...
a. -1024
b. 2048
c. -256
d. 128

Explanation:

Step1: Identify first term and ratio

First term $a_1 = 8$. Common ratio $r = \frac{-16}{8} = -2$.

Step2: Use geometric term formula

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$. For $n=9$:
$a_9 = 8 \cdot (-2)^{9-1}$

Step3: Calculate exponent and product

First compute $(-2)^8 = 256$. Then $a_9 = 8 \cdot 256 = 2048$.

Answer:

b. 2048