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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. 28 (page 824)

Find the indicated term of each geometric sequence.
$10 t h$ term of $- 1, 2, - 4, . . . . . .$

Short Answer

Expert verified

The $10 t h$ term is $512$ .

Step by step solution

01

Step 1. Given information.

We have, $- 1, 2, - 4, . . . . .$

$a_{1} = - 1, a_{2} = 2, a_{3} = - 4$

The common ratio is

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

The common ratio $r = - 2$

02

To find the 10th term.

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

Substitute $a_{1} = - 1, r = - 2$ and $n = 10$

role="math" localid="1647019188211" $a_{n} = a_{1} r^{10 - 1} a_{10} = (- 1) {(- 2)}^{9} a_{10} = 512$

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Most popular questions from this chapter

In Problems 71-82, find the sum of each sequence.

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In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

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