Q. 12.5 an=鈭�1nn2.Write the first five ... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.5 (page 1166)

$a_{n} = {(鈭� 1)}^{n} n^{2} .$ 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 $a_{n} = {(鈭� 1)}^{n} n^{2}$ are -1, 4, -9, 16 and -25

Step by step solution

Step 1. Given information

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

Step 2. Find the first term

$\begin{array}{l} Forthefirsttermsubstitute n = 1, \\ 鈬� a_{1} = {(鈭� 1)}^{1} 鈰� 1^{2} \\ = 鈭� 1 鈰� 1 \\ = 鈭� 1 \end{array}$

Step 3. Find the second term

$\begin{array}{l} Forthesecondtermsubstitute n = 2, \\ 鈬� a_{2} = {(鈭� 1)}^{2} 鈰� 2^{2} \\ = 1 鈰� 4 \\ = 4 \end{array}$

Step 4. Find the third term

$\begin{array}{l} Forthethirdtermsubstitute n = 3, \\ 鈬� a_{3} = {(鈭� 1)}^{3} 鈰� 3^{2} \\ = 鈭� 1 鈰� 9 \\ = 鈭� 9 \end{array}$

Step 5. Find the fourth term

$\begin{array}{l} Forthefourthtermsubstitute n = 4, \\ 鈬� a_{4} = {(鈭� 1)}^{4} 鈰� 4^{2} \\ = 1 鈰� 16 \\ = 16 \end{array}$

Step 6. Find the fifth term

$\begin{array}{l} Forthefifthtermsubstitute n = 5, \\ 鈬� a_{5} = {(鈭� 1)}^{5} 鈰� 5^{2} \\ = 鈭� 1 鈰� 25 \\ = 鈭� 25 \end{array}$

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91影视

$a_{n} = {(鈭� 1)}^{n} n^{2} .$ 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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91影视

an=鈭�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

Logic and Functions

Mechanics Maths

Pure Maths

Probability and Statistics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

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