Chapter 12: Q. 12.5 (page 1166)

$a_{n} = {(- 1)}^{n} n^{2} .$ Write the first five terms of the sequence whose general term is

Short Answer

Expert verified

The first five terms of the sequence with the general term as $a_{n} = {(- 1)}^{n} n^{2}$ are -1, 4, -9, 16 and -25

Step by step solution

Step 1. Given information

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

Step 2. Find the first term

$\begin{array}{l} Forthefirsttermsubstitute n = 1, \\ \Rightarrow a_{1} = {(- 1)}^{1} \cdot 1^{2} \\ = - 1 \cdot 1 \\ = - 1 \end{array}$

Step 3. Find the second term

$\begin{array}{l} Forthesecondtermsubstitute n = 2, \\ \Rightarrow a_{2} = {(- 1)}^{2} \cdot 2^{2} \\ = 1 \cdot 4 \\ = 4 \end{array}$

Step 4. Find the third term

$\begin{array}{l} Forthethirdtermsubstitute n = 3, \\ \Rightarrow a_{3} = {(- 1)}^{3} \cdot 3^{2} \\ = - 1 \cdot 9 \\ = - 9 \end{array}$

Step 5. Find the fourth term

$\begin{array}{l} Forthefourthtermsubstitute n = 4, \\ \Rightarrow a_{4} = {(- 1)}^{4} \cdot 4^{2} \\ = 1 \cdot 16 \\ = 16 \end{array}$

Step 6. Find the fifth term

$\begin{array}{l} Forthefifthtermsubstitute n = 5, \\ \Rightarrow a_{5} = {(- 1)}^{5} \cdot 5^{2} \\ = - 1 \cdot 25 \\ = - 25 \end{array}$

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$a_{n} = {(- 1)}^{n} n^{2} .$ Write the first five terms of the sequence whose general term is

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first term

Step 3. Find the second term

Step 4. Find the third term

Step 5. Find the fourth term

Step 6. Find the fifth term

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an=−1nn2.Write the first five terms of the sequence whose general term is

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first term

Step 3. Find the second term

Step 4. Find the third term

Step 5. Find the fourth term

Step 6. Find the fifth term

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Mechanics Maths

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

$a_{n} = {(- 1)}^{n} n^{2} .$ Write the first five terms of the sequence whose general term is