Q. 32 In the following exercise, find ... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 32 (page 1173)

In the following exercise, find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, 鈥�$

Short Answer

Expert verified

The general term for the sequence whose first five terms are $\frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, 鈥�$ is $a_{n} = \frac{1}{n^{3}} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thefirstfivetermsofthesequenceare \\ \frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, 鈥� \\ Wehavetofindthegeneraltermforthesequence. \end{array}$

Step 2. Observing the pattern

Now,

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms: & \frac{1}{1} & \frac{1}{8} & \frac{1}{27} & \frac{1}{64} & \frac{1}{125} & ... \\ Pattern & \frac{1}{1^{3}} & \frac{1}{2^{3}} & \frac{1}{3^{3}} & \frac{1}{4^{3}} & \frac{1}{5^{3}} & ... & \frac{1}{n^{3}} \end{matrix}$

Step 3. Conclusion

From the above table, we can observe that the general terms will be $a_{n} = \frac{1}{n^{3}} .$

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91影视

In the following exercise, find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, 鈥�$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Observing the pattern

Step 3. Conclusion

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91影视

In the following exercise, find a general term for the sequence whose first five terms are shown. 11,18,127,164,1125,鈥�

Short Answer

Step by step solution

Step 1. Given information

Step 2. Observing the pattern

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercise, find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{8}, \frac{1}{27}, \frac{1}{64}, \frac{1}{125}, 鈥�$