Chapter 7.9, Problem 6CYU

To determine

To Find: The next three terms of geometric sequence $100,50,\mathrm{25.....}$ .

Answer to Problem 6CYU

Next three terms of the sequence are: $\frac{25}{2},\frac{25}{4}\&\frac{25}{8}$

Explanation of Solution

Given information:

Geometric sequence is $100,50,\mathrm{25.....}$ .

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 $100,50,\mathrm{25.....}$

Common ratio is

  $\begin{array}{l}r=\frac{50}{100}=\frac{25}{50}=\frac{1}{2}\\ \text{Then next term three terms are}\\ 25\times \frac{1}{2}=\frac{25}{2}\\ \frac{25}{2}\times \frac{1}{2}=\frac{25}{4}\\ \frac{25}{4}\times \frac{1}{2}=\frac{25}{8}\end{array}$

Conclusion:

Next three terms of the sequence are: $\frac{25}{2},\frac{25}{4}\&\frac{25}{8}$