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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 154. (page 1198)

In the following exercises, find the indicated term of the given sequence. Find the general term for the sequence.
Find $a_{16}$ of the sequence, $224, - 112, 56, - 28, 14, - 7, . . .$

Short Answer

Expert verified

The value of $a_{16}$ is $- 0.0068359375$ and the general term for the sequence is $a_{n} = 224 {(- \frac{1}{2})}^{n - 1}$ .

Step by step solution

01

Step 1. Write the given information, determine the first term and find common ratio.

The given sequence is:

$224, - 112, 56, - 28, 14, - 7, . . .$

First term is:

$a_{1} = 224$

Common ratio:

$\frac{- 112}{224} = - \frac{1}{2}, \frac{56}{- 112} = - \frac{1}{2}, \frac{- 28}{56} = - \frac{1}{2}, \frac{- 7}{14} = - \frac{1}{2} r = - \frac{1}{2}$

02

Step 2. Use the formula of general term to find the sixteenth term

$a_{n} = a_{1} r^{n - 1}$

Substitute $a_{1} = 224, r = - \frac{1}{2}$ and $n = 16$

role="math" localid="1645357589753" $a_{16} = (224) {(- \frac{1}{2})}^{16 - 1} = (224) {(- \frac{1}{2})}^{15} = - 0.0068359375$

$a_{16} = - 0.0068359375$

03

Step 3. Find the general term.

Substitute $a_{1} = 224$ and $r = - \frac{1}{2}$ in the formula,

$a_{n} = a_{1} r^{n - 1} a_{n} = 224 {(- \frac{1}{2})}^{n - 1}$

The general term of the sequence is $a_{n} = 224 {(- \frac{1}{2})}^{n - 1}$ .

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Most popular questions from this chapter

In the following exercises, evaluate.
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