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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 26. (page 808)

In Problems 17鈥�28, write down the first five terms of each sequence.
$\{a_{n}\} = \{\frac{3^{n}}{n}\}$

Short Answer

Expert verified

The first five terms of the given sequence are $3, \frac{9}{2}, 9, \frac{81}{4}, \frac{243}{5}$

Step by step solution

01

Step 1. Write the given sequence.

The given sequence is $\{a_{n}\} = \{\frac{3^{n}}{n}\}$

02

Step 2. Find the five terms.

To find the five terms in the sequence we substitute $1, 2, 3, 4 a n d 5 i n t o n$

$\{a_{1}\} = \{\frac{3^{1}}{1}\} = 3 \{a_{2}\} = \{\frac{3^{2}}{2}\} = \frac{9}{2} \{a_{3}\} = \{\frac{3^{3}}{3}\} = 9 \{a_{4}\} = \{\frac{3^{4}}{3}\} = \frac{81}{4} \{a_{5}\} = \{\frac{3^{5}}{5}\} = \frac{243}{5}$

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Most popular questions from this chapter

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

$3 + \frac{3^{2}}{2} + \frac{3^{3}}{3} + . . . . . + \frac{3^{n}}{n}$

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

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

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

$1 - \frac{3}{4} + \frac{9}{16} - \frac{27}{64} + . . . .$

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

$\frac{1}{e} + \frac{2}{e^{2}} + \frac{3}{e^{3}} + . . . . . . . . . + \frac{n}{e^{n}}$

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

$\frac{2}{3} - \frac{4}{9} + \frac{8}{27} - . . . . . . . . + {(- 1)}^{12} {(\frac{2}{3})}^{11}$

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