Chapter 7, Problem 85CR

To determine

To write the recursive formula for the geometric sequence $10,1,0.1,0.01,\mathrm{..........}$

Answer to Problem 85CR

  $a_1=10;a_n=\left(0.1\right)a_{n-1}$

Explanation of Solution

Given:

  $10,1,0.1,0.01,\mathrm{..........}$

Calculation:

The starting value $a_1$ is 10.

The common ratio $r$ is $\frac{1}{10}=0.1$ .

Now the recursive formula is,

  $\begin{array}{l}{a}_1=a;a_n=a_{n-1}\cdot r\\ \Rightarrow a_1=10;a_n=a_{n-1}\cdot \left(0.1\right)\\ \Rightarrow a_1=10;a_n=\left(0.1\right)a_{n-1}\end{array}$