Q. 18 In the following exercise, write... [FREE SOLUTION]

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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. 18 (page 1173)

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{{(鈭� 1)}^{n + 1}}{2 n}$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = \frac{{(鈭� 1)}^{n + 1}}{2 n}$ are $\frac{1}{2}, \frac{鈭� 1}{4}, \frac{1}{6}, \frac{鈭� 1}{8}, \frac{1}{10} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermisgivenas \\ a_{n} = \frac{{(鈭� 1)}^{n + 1}}{2 n} \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Calculating the terms

$\begin{array}{l} Wewillsubstitute n = 1, 2, 3, 4 and 5 inordertofindtheterms. \\ Now, \end{array}$

localid="1645363645833" $\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = \frac{{(鈭� 1)}^{1 + 1}}{2 (1)} \\ = \frac{{(鈭� 1)}^{2}}{2} \\ = \frac{1}{2} \end{array} & \begin{array}{l} a_{2} = \frac{{(鈭� 1)}^{2 + 1}}{2 (2)} \\ = \frac{{(鈭� 1)}^{3}}{4} \\ = \frac{鈭� 1}{4} \end{array} & \begin{array}{l} a_{3} = \frac{{(鈭� 1)}^{3 + 1}}{2 (3)} \\ = \frac{{(鈭� 1)}^{4}}{6} \\ = \frac{1}{6} \end{array} & \begin{array}{l} a_{4} = \frac{{(鈭� 1)}^{4 + 1}}{2 (4)} \\ = \frac{{(鈭� 1)}^{5}}{8} \\ = \frac{鈭� 1}{8} \end{array} & \begin{array}{l} a_{5} = \frac{{(鈭� 1)}^{5 + 1}}{2 (5)} \\ = \frac{{(鈭� 1)}^{6}}{10} \\ = \frac{1}{10} \end{array} \end{matrix}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $\frac{1}{2}, \frac{鈭� 1}{4}, \frac{1}{6}, \frac{鈭� 1}{8}, \frac{1}{10} .$

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91影视

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{{(鈭� 1)}^{n + 1}}{2 n}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

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91影视

In the following exercise, write the first five terms of the sequence whose general term is given.an=鈭�1n+12n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

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In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{{(鈭� 1)}^{n + 1}}{2 n}$