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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 30. (page 824)

Find the indicated term of each geometric sequence.
$7 t h$ term of $0.1, 1.0, 10.0, . . . . .$

Short Answer

Expert verified

The $7 t h$ term is $10^{5}$ .

Step by step solution

01

Step 1. Given information.

We have, $0.1, 1.0, 10.0, . . . . .$

$a_{1} = 0.1, a_{2} = 1.0, a_{3} = 10.0$

The common ratio is

$\frac{a_{2}}{a_{1}} = \frac{1.0}{0.1} = 10 \frac{a_{3}}{a_{2}} = \frac{10.0}{1.0} = 10$

The common ratio $r = 10$ .

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 $a_{1} = 0.1, r = 10$ and $n = 7$

$a_{7} = (0.1) {(10)}^{7 - 1} a_{7} = (0.1) {(10)}^{6} a_{7} = 10^{5}$

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