Chapter 12: Q. 12.6 (page 1166)

Write the first five terms of the sequence whose general term is $a_{n} = {(- 1)}^{n + 1} n^{3}$

Short Answer

Expert verified

The first five terms of the sequence with the general term as $a_{n} = {(- 1)}^{n + 1} n^{3}$ are 1, -8, 27, -64 and 125

Step by step solution

Step 1. Given information

$\begin{array}{l} Theexpressionforthegeneraltermsisgivenas \\ a_{n} = {(- 1)}^{n + 1} n^{3} \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Calculating the terms

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 \\ a_{n} & \begin{array}{l} a_{1} = {(- 1)}^{1 + 1} \cdot 1^{3} \\ = {(- 1)}^{2} \cdot 1 \\ = 1 \cdot 1 \\ = 1 \end{array} & \begin{array}{l} a_{2} = {(- 1)}^{2 + 1} \cdot 2^{3} \\ = {(- 1)}^{3} \cdot 8 \\ = - 1 \cdot 8 \\ = - 8 \end{array} & \begin{array}{l} a_{3} = {(- 1)}^{3 + 1} \cdot 3^{3} \\ = {(- 1)}^{4} \cdot 27 \\ = 1 \cdot 27 \\ = 27 \end{array} & \begin{array}{l} a_{4} = {(- 1)}^{4 + 1} \cdot 4^{3} \\ = {(- 1)}^{5} \cdot 64 \\ = - 1 \cdot 64 \\ = - 64 \end{array} & \begin{array}{l} a_{5} = {(- 1)}^{5 + 1} \cdot 5^{3} \\ = {(- 1)}^{6} \cdot 125 \\ = 1 \cdot 125 \\ = 125 \end{array} \end{array}$

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Write the first five terms of the sequence whose general term is $a_{n} = {(- 1)}^{n + 1} n^{3}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

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Write the first five terms of the sequence whose general term isan=−1n+1n3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

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Most popular questions from this chapter

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Write the first five terms of the sequence whose general term is $a_{n} = {(- 1)}^{n + 1} n^{3}$