Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

68 is the _? th term of the arithmetic sequence -2, 3, 8, ... .

68 is the 15th term of the arithmetic sequence -2, 3, 8, ....

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given arithmetic sequence is -2, 3, 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 $a_{1} = - 2$

The difference between the first two terms is $3 - (- 2) = 3 + 2 = 5$

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

The common difference is $d = 5$

The given nth term is $a_{n} = 68$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 68 = - 2 + (n - 1) (5) \\ 68 + 2 = (n - 1) (5) \\ (n - 1) (5) = 70 \\ n - 1 = \frac{70}{5} \\ n - 1 = 14 \\ n = 14 + 1 \\ n = 15 \end{array}$

Step 3. Conclusion.

Hence, 68 is the 15^th term of the arithmetic sequence -2, 3, 8, ... .

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68 is the _? th term of the arithmetic sequence -2, 3, 8, ... .

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Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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68 is the _? th term of the arithmetic sequence -2, 3, 8, ... .