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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 23. (page 824)

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given
$a_{1} = \sqrt{2}, r = \sqrt{2}$

Short Answer

Expert verified

The $n t h$ term is $a_{n} = {\sqrt{2}}^{n}$ and the fifth term is $a_{5} = 4 \sqrt{2}$ .

Step by step solution

01

Step 1. Given information.

We have,

$a_{1} = \sqrt{2}, r = \sqrt{2}$

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

02

Step 2. To find the fifth term and the nth term.

Substitute $a_{1} = \sqrt{2}, r = \sqrt{2}$ and $n = 5$

$a_{n} = \sqrt{2} {(\sqrt{2})}^{n - 1} a_{n} = {\sqrt{2}}^{n}$

and

role="math" localid="1647002123469" $a_{5} = \sqrt{2} {(\sqrt{2})}^{5 - 1} a_{5} = \sqrt{2} {(\sqrt{2})}^{4} a_{5} = 4 \sqrt{2}$

a_{1} = \sqrt{2}, r = \sqrt{2}

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Most popular questions from this chapter

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

$1, - 1, 1, - 1, 1, - 1, . . .$

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

role="math" localid="1646738671855" $\frac{1}{1 路 2}, \frac{1}{2 路 3}, \frac{1}{3 路 4}, \frac{1}{4 路 5}, . . .$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{t_{n}\} = \{\frac{{(- 1)}^{n}}{(n + 1 (n + 2)}\}$

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, . . .$

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

$a_{1} = \sqrt{2}; a_{n} = \sqrt{2 + a_{n - 1}}$

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