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Q43.

Expert-verified

Algebra 2

Found in: Page 582

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Complete the statement for each arithmetic sequence.
170 is the _? term of -4, 2, 8, ... .

170 is the 30th term of the arithmetic sequence -4, 2, 8, … .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given arithmetic sequence is -4, 2, 8, ...

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_{n} = a_{1} + (n - 1) d$ .

Here the first term is $a_{1} = - 4$

The difference between the first two terms is $2 - (- 4) = 2 + 4 = 6$

The difference between the second two terms is $8 - 2 = 6$

The common difference is $d = 6$

The given nth term is $a_{n} = 170$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 170 = - 4 + (n - 1) (6) \\ 170 + 4 = (n - 1) (6) \\ (n - 1) (6) = 174 \\ n - 1 = \frac{174}{6} \\ n - 1 = 29 \\ n = 29 + 1 \\ n = 30 \end{array}$

Step 3. Conclusion.

Hence, 170 is the 30th term of the arithmetic sequence -4, 2, 8, … .

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