Chapter 7.9, Problem 21PPS

To determine

To Find: The next three terms of geometric sequence $36,12,\mathrm{4.....}$ .

Answer to Problem 21PPS

Next three terms of the sequence are: $\frac{4}{3},\frac{4}{9}\&\frac{4}{27}$

Explanation of Solution

Given information:

Geometric sequence is $36,12,\mathrm{4.....}$ .

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 $36,12,\mathrm{4.....}$

Common ratio is

  $\begin{array}{l}r=\frac{12}{36}=\frac{4}{12}=\frac{1}{3}\\ \text{Then next term three terms are}\\ 4\times \frac{1}{3}=\frac{4}{3}\\ \frac{4}{3}\times \frac{1}{3}=\frac{4}{9}\\ \frac{4}{9}\times \frac{1}{3}=\frac{4}{27}\end{array}$

Conclusion:

Next three terms of the sequence are: $\frac{4}{3},\frac{4}{9}\&\frac{4}{27}$