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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.10 (page 1167)

Find a general term for the sequence whose first five terms are shown 1, −4, 9, −16, 25,...

Short Answer

Expert verified

The general term for the given sequence is $a_{n} = {(- 1)}^{n + 1} n^{2}$

Step by step solution

01

Step 1. Given information

The first five terms are shown 1, −4, 9, −16, 25,

02

Step 2. Observing the pattern

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & 1 & - 4 & 9 & - 16 & 25 & ... \\ Pattern & {(- 1)}^{1 + 1} 1^{2} & {(- 1)}^{1 + 2} 2^{2} & {(- 1)}^{3} 3^{3} & {(- 1)}^{4 + 1} 4^{2} & {(- 1)}^{5 + 1} 5^{2} & ... & {(- 1)}^{n + 1} n^{2} \end{array}$

03

Step 3. Conclusion

The numbers are powers of 2. The signs are alternating, with even $n$ negative.

Therefore, the general term for the given sequence islocalid="1645103580853" $a_{n} = {(- 1)}^{n + 1} n^{2}$

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Most popular questions from this chapter

In the following exercises, expand each binomial using Pascal's Triangle.

$(z - 3)^{5}$

Determine if each sequence is arithmetic. If so, indicate the common difference.

$\begin{array}{l} (a) 9, 20, 31, 42, 53, 64, \dots \\ (b) 12, 6, 0, - 6, - 12, - 18, \dots \\ (c) 7, 1, 10, 4, 13, 7, \dots \end{array}$

Write the first five terms of the sequence whose general term is $a_{n} = 2^{n} - 5$

Find the eleventh term of the sequence $7, 14, 28, 56, 112, 224, \dots$ Then find the general term for the sequence.

In the following exercises, expand each binomial using Pascal's Triangle.

$(3 x - 4)^{4}$

See all solutions

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