Chapter 7, Problem 32PT

To determine

To find the next three terms of the given geometric sequence.

Answer to Problem 32PT

Next three terms are $\frac{1}{2},\frac{1}{8},\frac{1}{32}$ .

Explanation of Solution

Given:

  $32,8,2,\mathrm{......}$

Concept used:

The n^th term of a geometric sequence with first term ‘a’ and common ratio ‘r’ is

  $a_n=a{r}^{n-1}$

Calculation:

  $32,8,2,\mathrm{......}$

Given sequence is a geometric sequence with

  $a=32,r=\frac{8}{32}=\frac{1}{4}$

Therefore next three terms are

  $\begin{array}{l}{a}_4=a{r}^3=32{\left(\frac{1}{4}\right)}^3=\frac{32}{64}=\frac{1}{2}\\ a_5=a{r}^4=32{\left(\frac{1}{4}\right)}^4=\frac{32}{256}=\frac{1}{8}\\ a_6=a{r}^5=32{\left(\frac{1}{4}\right)}^5=\frac{32}{1024}=\frac{1}{32}\end{array}$