Chapter 7.9, Problem 25PPS

To determine

To Find: The next three terms of geometric sequence $1024,-128,\mathrm{16.....}$ .

Answer to Problem 25PPS

Next three terms of the sequence are: $-2,\frac{1}{4}\&-\frac{1}{32}$

Explanation of Solution

Given information:

Geometric sequence is $1024,-128,\mathrm{16.....}$ .

Concept and Formula Used:

Geometric Sequence: Sequence in which each term after the first is found by multiplying the previous term by a constant called common ratio.

Calculation:

It is given that geometric sequence $1024,-128,\mathrm{16.....}$

Common ratio is

  $\begin{array}{l}r=\frac{-128}{1024}=\frac{16}{-128}=-\frac{1}{8}\\ \text{Then next term three terms are}\\ 16\times -\frac{1}{8}=-2\\ -2\times -\frac{1}{8}=\frac{1}{4}\\ \frac{1}{4}\times -\frac{1}{8}=-\frac{1}{32}\end{array}$

Conclusion:

Next three terms of the sequence are: $-2,\frac{1}{4}\&-\frac{1}{32}$