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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 32. (page 809)

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
$\frac{2}{3}, \frac{4}{9}, \frac{8}{27}, \frac{16}{81}, . . .$

Short Answer

Expert verified

The nth term of the given sequence is $a_{n} = {(\frac{2}{3})}^{n}$

Step by step solution

01

Step 1. Write the given information.

The given sequence is:

$\frac{2}{3}, \frac{4}{9}, \frac{8}{27}, \frac{16}{81}, . . .$

02

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

$a_{1} = \frac{2}{3}, a_{2} = \frac{4}{9}, a_{3} = \frac{8}{27}, a_{4} = \frac{16}{81}, . . .$

The pattern of the sequence is:

$a_{1} = {(\frac{2}{3})}^{1} = \frac{2}{3} a_{2} = {(\frac{2}{3})}^{2} = \frac{4}{9} a_{3} = {(\frac{2}{3})}^{3} = \frac{8}{27} a_{4} = {(\frac{2}{3})}^{4} = \frac{16}{81} a_{n} = {(\frac{2}{3})}^{n}$

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Most popular questions from this chapter

True or False. The notation $a_{5}$ represents the fifth term of a sequence.

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

$\{S_{n}\} = \{\frac{2^{n}}{3^{n} + 1}\}$

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

${鈭�}_{k = 1}^{鈭�} 3 {(\frac{3}{2})}^{k - 1}$

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

${鈭�}_{k = 0}^{n} {(\frac{3}{2})}^{k}$

In Problems 11鈥�16, evaluate each factorial expression.

$\frac{5! 8!}{3!}$

See all solutions

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