Chapter 7, Problem 72SGR

To determine

The next three terms of the given geometric sequence.

Answer to Problem 72SGR

The next three terms of the geometric sequence are 32, 16, 8.

Explanation of Solution

Given information:The geometric sequence given 256, 128, 64, …

Calculation:

The first term of the geometric sequence is $a_1=256$ .

Second term is $a_2=128$ , third term is $a_3=64$

We know that, common ratio = r = $\frac{a_2}{a_1}=\frac{a_3}{a_2}$ .

  $\therefore r=\frac{128}{256}=\frac{64}{128}=\frac{1}{2}$

$\therefore$ The fourth term

  $a_4=a_3\cdot r=a_3\cdot \frac{1}{2}=64\cdot \frac{1}{2}=32$

The fifth term

  $a_5=a_4\cdot r=a_4\cdot \frac{1}{2}=32\cdot \frac{1}{2}=16$

The sixth term

  $a_6=a_5\cdot r=a_5\cdot \frac{1}{2}=16\cdot \frac{1}{2}=8$

$\therefore$ The next three terms are 32, 16, 8.