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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 31. (page 825)

In Problems 31鈥�38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$7, 14, 28, 56, . . .$

Short Answer

Expert verified

The common ratio is $r = 2$ and the nth term is $a_{n} = 7 路 {(2)}^{n - 1}$

Step by step solution

01

Step 1. Write the given information.

The given geometric sequence is $7, 14, 28, 56, . . .$

02

Step 2. Find the common ratio.

$a_{1} = 7, a_{2} = 14, a_{3} = 28 \frac{a_{2}}{a_{1}} = \frac{14}{7} = 2 \frac{a_{3}}{a_{2}} = \frac{28}{14} = 2 r = 2$

03

Step 3. Find the nth term.

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

The nth term is $a_{n} = 7 路 {(2)}^{n - 1}$

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Most popular questions from this chapter

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

${鈭�}_{k = 0}^{n - 1} (2 k + 1)$

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

$a_{1} = 2; a_{n} = - a_{n - 1}$

For the function $f (x) = \frac{x - 1}{x},$ find $f (2) a n d f (3)$ .

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