Chapter 7.9, Problem 23PPS

To determine

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

Answer to Problem 23PPS

Next three terms are 6.25, 1.5625 and 0.390625.

Explanation of Solution

Given:

  $400,100,25,\mathrm{......}$

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:

  $400,100,25,\mathrm{......}$

Given sequence is a geometric sequence with

  $a=400,r=\frac{100}{400}=\frac{1}{4}$

Therefore next three terms are

  $\begin{array}{l}{a}_4=a{r}^3=400{\left(\frac{1}{4}\right)}^3=\frac{400}{64}=6.25\\ a_5=a{r}^4=400{\left(\frac{1}{4}\right)}^4=\frac{400}{256}=1.5625\\ a_6=a{r}^5=400{\left(\frac{1}{4}\right)}^5=\frac{400}{1024}=0.390625\end{array}$