Short Answer

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, . . .$

The nth term of the given sequence is $a_{n} = \frac{1}{2^{n - 1}}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information.

The given sequence is:

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

Step 2. Determine the pattern of the sequence and write down the nth term.

$a_{1} = 1, a_{2} = \frac{1}{2}, a_{3} = \frac{1}{4}, a_{4} = \frac{1}{8}$

The pattern of the sequence is:

$a_{1} = \frac{1}{2^{1} - 1} = 1 a_{2} = \frac{1}{2^{2 - 1}} = \frac{1}{2} a_{3} = \frac{1}{2^{3 - 1}} = \frac{1}{4} a_{4} = \frac{1}{2^{4 - 1}} = \frac{1}{8} a_{n} = \frac{1}{2^{n - 1}}$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, . . .$

Step by Step Solution

Step 1. Write the given information.

Step 2. Determine the pattern of the sequence and write down the nth term.

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Precalculus Enhanced with Graphing Utilities

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In Problems 29–36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.1, 12, 14, 18, ...

Step by Step Solution

Step 1. Write the given information.

Step 2. Determine the pattern of the sequence and write down the nth term.

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In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, . . .$