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Q44.

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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.
124 is the _? term of -2, 5, 12, ... .

124 is the 19th term of the arithmetic sequence -2, 5, 12, … .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given arithmetic sequence is -2, 5, 12, ...

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 $a_{1} = - 2$

The difference between the first two terms is $5 - (- 2) = 5 + 2 = 7$

The difference between the second two terms is $12 - 5 = 7$

The common difference is $d = 7$

The given nth term is $a_{n} = 124$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 124 = - 2 + (n - 1) (7) \\ 124 + 2 = (n - 1) (7) \\ (n - 1) (7) = 126 \\ n - 1 = \frac{126}{7} \\ n - 1 = 18 \\ n = 18 + 1 \\ n = 19 \end{array}$

Step 3. Conclusion.

Hence, 124 is the 19th term of the arithmetic sequence -2, 5, 12, … .

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