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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. 277 (page 1219)

In the following exercises, find each sum.
${鈭�}_{i = 1}^{50} (4 i - 5)$

Short Answer

Expert verified

The sum is equal to $4850$ .

Step by step solution

01

Step 1. Given Information

We are given,

${鈭�}_{i = 1}^{50} (4 i - 5)$

We have to find the given sum.

02

Step 2. Finding the terms

The terms is given by putting $i = 1, 2, 3 . . . . 50$

${鈭�}_{i = 1}^{50} (4 i - 5) = (4 路 1 - 5) + (4 路 2 - 5) + (4 路 3 - 5) + 鈥� + (4 路 50 - 5) {鈭�}_{i = 1}^{50} (4 i - 5) = (4 - 5) + (8 - 5) + (12 - 5) + 鈥� + (200 - 5) {鈭�}_{i = 1}^{50} (4 i - 5) = - 1 + 3 + 7 + 鈥� + 195$

So, the first term is $- 1$ and the fifth term is $195$ .

03

Step 3. Finding the sum

Putting the values in formula, we get

$S_{n} = \frac{n}{2} (a + a_{n}) S_{50} = \frac{50}{2} (- 1 + 195) S_{50} = 25 (194) S_{50} = 4850$

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Most popular questions from this chapter

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

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Write the first five terms of the sequence whose general term is $a_{n} = 3^{n} + 4$

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