Chapter 7.8, Problem 30PPE

To determine

To Write: Write the explicit and recursive formula for the given geometric sequence.

Answer to Problem 30PPE

The recursive formula is $a_n=a_{n-1}.\left(\frac{1}{2}\right);a_1=100$

Explanation of Solution

Given information : The given sequence is $100,50,25,12.5,\mathrm{...}$

Here the geometric sequence is $100,50,25,12.5,\mathrm{...}$

Here the first term is $a_1=100$ and common ratio = $r=\frac{50}{100}=\frac{1}{2}$

The recursive formula is

  $a_n=a_{n-1}.r;a_1=100$

Now, substituting the value of r

  $a_n=a_{n-1}.\left(\frac{1}{2}\right);a_1=100$