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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 34. (page 825)

In Problems 31鈥�38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

Short Answer

Expert verified

The common ratio is $r = \frac{1}{4}$ and the nth term is $4 路 {\frac{1}{4}}^{n - 1}$

Step by step solution

01

Step 1. Write the given information.

The geometric sequence is $4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

02

Step 2. Find the common ratio.

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

03

Step 3. Find the nth term.

The formula for the nth term is $a_{n} = a_{1} 路 r^{n - 1}$

$a_{n} = 4 路 {\frac{1}{4}}^{n - 1}$

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Most popular questions from this chapter

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$1 + \frac{1}{3} + \frac{1}{9} + . . . . .$

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

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

Find x so that x, x + 2, and x + 3 are consecutive terms of a geometric sequence.

In Problems 51鈥�60, write out each sum.

${鈭�}_{k = 0}^{n - 1} (2 k + 1)$

In Problems 61鈥�70, express each sum using summation notation.

$1 + 2 + 3 + . . . + 20$

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