Question

Use the information given to identify the ...... term of the geometric sequence:

Answer 1

\[a _{2}=1/2.......r=2\]

Answer 2

\[a _{9}=256, 128, 512, 64\]

Answer 3

$$
a_n = c \cdot r^n \\
r = 2 \implies a_n = c \cdot 2^n \\
n = 2 \implies a_2 = c \cdot 2^2 \implies \frac{1}{2} = c \cdot4 \\
c = \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8} \\
a_n = \frac{2^n}{8} = \frac{2^n}{2^3} = 2^{n-3}\\
a_9 = 2^{9-3} = 2^6 = 64
$$