Chapter 12: Q. 11 (page 1173)

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{4 n - 2}{2^{n}}$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = \frac{4 n - 2}{2^{n}}$ are $1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \frac{9}{16} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermforthesequenceisgivenas \\ a_{n} = \frac{4 n - 2}{2^{n}} \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Calculating the terms

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

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = \frac{4 (1) - 2}{2^{1}} \\ = \frac{4 - 2}{2} \\ = \frac{2}{2} \\ = 1 \end{array} & \begin{array}{l} a_{2} = \frac{4 (2) - 2}{2^{2}} \\ = \frac{8 - 2}{4} \\ = \frac{6}{4} \\ = \frac{2}{3} \end{array} & \begin{array}{l} a_{3} = \frac{4 (3) - 2}{2^{3}} \\ = \frac{12 - 2}{8} \\ = \frac{10}{8} \\ = \frac{5}{4} \end{array} & \begin{array}{l} a_{4} = \frac{4 (4) - 2}{2^{4}} \\ = \frac{16 - 2}{32} \\ = \frac{14}{16} \\ = \frac{7}{8} \end{array} & \begin{array}{l} a_{5} = \frac{4 (5) - 2}{2^{5}} \\ = \frac{20 - 2}{32} \\ = \frac{18}{32} \\ = \frac{9}{16} \end{array} \end{matrix}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \frac{9}{16} .$

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In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{4 n - 2}{2^{n}}$

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.an=4n−22n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{4 n - 2}{2^{n}}$