Chapter 12: Q. 13 (page 1173)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermisgivenas \\ a_{n} = {(- 1)}^{n} \cdot 2 n \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Calculating the terms

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

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = {(- 1)}^{1} \cdot 2 (1) \\ = - 1 \cdot 2 \\ = - 2 \end{array} & \begin{array}{l} a_{2} = {(- 1)}^{2} \cdot 2 (2) \\ = 1 \cdot 4 \\ = 4 \end{array} & \begin{array}{l} a_{3} = {(- 1)}^{3} \cdot 2 (3) \\ = - 1 \cdot 6 \\ = - 6 \end{array} & \begin{array}{l} a_{4} = {(- 1)}^{4} \cdot 2 (4) \\ = 1 \cdot 8 \\ = 8 \end{array} & \begin{array}{l} a_{5} = {(- 1)}^{5} \cdot 2 (5) \\ = - 1 \cdot 10 \\ = - 10 \end{array} \end{matrix}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $- 2, 4, - 6, 8, - 10.$

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

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=(-1)n·2n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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