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Q38.

Expert-verified

Algebra 2

Found in: Page 581

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the indicated term of each arithmetic sequence.
$a_{12}$ for 8, 3, -2, …

The indicated term of the arithmetic sequence is -47.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given arithmetic sequence is 8, 3, -2, …

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 $a_{1} = 8$

The difference between the first two terms is $3 - 8 = - 5$

The difference between the next two terms is $- 2 - 3 = - 5$

The common difference is $d = - 5$

And the required term is $n = 12$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{12} = 8 + (12 - 1) (- 5) \\ a_{12} = 8 + (11) (- 5) \\ a_{12} = 8 - 55 \\ a_{12} = - 47 \end{array}$

Step 3. Conclusion.

Hence, the indicated term of the arithmetic sequence is -47.

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