Chapter 12: Q. 12.12 (page 1167)

Find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \dots$

Short Answer

Expert verified

The general term for the given sequence is $a_{n} = \frac{1}{n^{2}}$ .

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivensequenceis \\ \frac{1}{1}, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \dots \\ Wehavetofindthegeneraltermforthegivensequence. \end{array}$

Step 2. Observing the pattern

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & \frac{1}{1} & \frac{1}{4} & \frac{1}{9} & \frac{1}{16} & \frac{1}{25} & ... \\ Pattern & \frac{1}{1^{2}} & \frac{1}{2^{2}} & \frac{1}{3^{2}} & \frac{1}{4^{2}} & \frac{1}{5^{2}} & ... & \frac{1}{n^{2}} \end{array}$

Step 3. Conclusion

From the table in the above step, we can observe that the numerators are all 1. The denominator is the square of the number of terms.

Therefore,

The general term of the given sequence can be written as $a_{n} = \frac{1}{n^{2}} .$

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Find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \dots$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Observing the pattern

Step 3. Conclusion

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Find a general term for the sequence whose first five terms are shown.11,14,19,116,125,…

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

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Study anywhere. Anytime. Across all devices.

Find a general term for the sequence whose first five terms are shown.
$\frac{1}{1}, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \dots$