Chapter 7, Problem 9CT

To determine

To write the recursive formula for the geometric sequence $10,40,160,640,\mathrm{..........}$

Answer to Problem 9CT

  $a_1=10;a_n=4a_{n-1}$

Explanation of Solution

Given:

  $10,40,160,640,\mathrm{..........}$

Calculation:

The starting value $a_1$ is 10.

The common ratio $r$ is $\frac{40}{10}=4$ .

Now the recursive formula is,

  $\begin{array}{l}{a}_1=a;a_n=a_{n-1}\cdot r\\ \Rightarrow a_1=10;a_n=a_{n-1}\cdot 4\\ \Rightarrow a_1=10;a_n=4a_{n-1}\end{array}$