Question

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

Answer 1

The n-th term of a geometric sequence is given by the formula:

`\begin{gathered} U_n=a_1r^(n-1) \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}`

Given that:

`\begin{gathered} a_2=64 \\ r=(1)/(4) \\ n=2 \end{gathered}`

Hence,

`\begin{gathered} a_2=a_1((1)/(4))^(2-1)=64 \\ a_1((1)/(4))=64 \\ a_1=64*4 \\ =256 \end{gathered}`

Therefore, the rule for the nth term of the sequence is

`\begin{gathered} U_n=a_1r^(n-1) \\ U_n=256_{}((1)/(4))^(n-1) \end{gathered}`