Question

Write a rule for the nth term of the geometric sequence given a_2=64, r=1/4

Answer 1

To write a general rule for a geometric sequence you need to find the first term a1. Use the given term and the common ratio to find it:

`\begin{gathered} a_n=a_1\cdot r^(n-1) \\ \\ a_2=64 \\ n=2 \\ r=(1)/(4) \\ \\ 64=a_1\cdot((1)/(4))^(2-1) \\ \\ 64=a_1((1)/(4))^1 \\ \\ 64=a_1((1)/(4)) \\ 64\cdot4=a_1 \\ 256=a_1 \end{gathered}`

Then, with a1 and the common ratio you get the next general rule:

`a_n=256\cdot((1)/(4))^(n-1)`