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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.23 (page 1171)

Write each sum using summation notation: 1 − 4 + 9 − 16 + 25.

Short Answer

Expert verified

The sum written in summation notation is

$1 - 4 + 9 - 16 + 25 = \sum_{n = 1}^{5} {(- 1)}^{n + 1} n^{2} .$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivensumis \\ 1 - 4 + 9 - 16 + 25 \\ Wehavetowritethesumusingsummationnotation. \end{array}$

02

Step 2. Find the pattern

Now,

We look for a pattern in the terms.

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

03

Step 3. Conclusion

From the above table, we can observe that the general term is ${(- 1)}^{n + 1} n^{2}$

Therefore,

The sum of $1 - 4 + 9 - 16 + 25$ can be written in the form of summation notation as $\sum_{n = 1}^{5} {(- 1)}^{n + 1} n^{2} .$

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Most popular questions from this chapter

Write the first five terms of the sequence where the first term is 7 and the common difference is $d = - 4$ .

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find $a_{11}$ given $a_{1} = 8$ and $r = 3$ .

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, find the indicated term of a sequence where the first term and the common ratio is given.

Find $a_{13}$ given $a_{1} = 7$ and $r = 2$ .

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = - 5$ and $r = - 3$

See all solutions

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