Chapter 7.9, Problem 7CYU

To determine

To Find: The next three terms of geometric sequence $4,-1,\frac{1}{4}\mathrm{.....}$ .

Answer to Problem 7CYU

Next three terms of the sequence are: $-\frac{1}{16},\frac{1}{64}\&-\frac{1}{256}$

Explanation of Solution

Given information:

Geometric sequence $4,-1,\frac{1}{4}\mathrm{.....}$ .

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 $4,-1,\frac{1}{4}\mathrm{.....}$

Common ratio is

  $\begin{array}{l}r=\frac{-1}{4}=\frac{\frac{1}{4}}{-1}=-\frac{1}{4}\\ \text{Then next term three terms are}\\ \frac{1}{4}\times -\frac{1}{4}=-\frac{1}{16}\\ -\frac{1}{16}\times -\frac{1}{4}=\frac{1}{64}\\ \frac{1}{64}\times -\frac{1}{4}=-\frac{1}{256}\end{array}$

Conclusion:

Next three terms of the sequence are: $-\frac{1}{16},\frac{1}{64}\&-\frac{1}{256}$