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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 25 (page 824)

Find the indicated term of each geometric sequence.
$7 t h$ term of $1, \frac{1}{2}, \frac{1}{4}, . . . . . .$

Short Answer

Expert verified

The $7 t h$ term is $a_{7} = \frac{1}{64}$ .

Step by step solution

01

Step 1. Given information.

We have, $1, \frac{1}{2}, \frac{1}{4}, . . . . . . .$

$a_{1} = 1, a_{2} = \frac{1}{2}, a_{3} = \frac{1}{4}$

The common ratio is

$\frac{a_{2}}{a_{1}} = \frac{\frac{1}{2}}{1} = \frac{1}{2} \frac{a_{3}}{a_{2}} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}$

Thus, the common ratio $r = \frac{1}{2}$

02

To find the 7th term.

The $n t h$ term of a geometric sequence is determined by formula $a_{n} = a_{1} r^{n - 1}$

Substitute $a_{1} = 1, r = \frac{1}{2}$ and $n = 7$ .

$a_{7} = 1 {(\frac{1}{2})}^{7 - 1} a_{7} = {(\frac{1}{2})}^{6} a_{7} = \frac{1}{64}$

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