Chapter 7.8, Problem 39PPE

To determine

To Write: Write the explicit and recursive formula if given sequence is a geometric sequence.

Answer to Problem 39PPE

It is not a geometric sequence.

Explanation of Solution

Given information : The given sequence is $20,15,10,5,\mathrm{...}$

We have the given sequence is $20,15,10,5,\mathrm{...}$

A sequence is said to be geometric sequence if each term is obtained by multiplying the common ratio to the previous term.

Here the first term is $a_1=20$ and common ratio = $\frac{15}{20}=\frac{3}{4}$

Now, $a_2=a_{1}r=20\times \frac{3}{4}=15$

  $a_3=a_{2}r=15\times \frac{3}{4}\ne 10$ and so on

Therefore, the given sequence is not a geometric sequence.