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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.40. (page 1183)

Find the sum: $\sum_{i = 1}^{35} (5 i - 3)$

Short Answer

Expert verified

The obtained sum is 3045.

Step by step solution

01

Step 1. Given information.

The given sum expression is $\sum_{i = 1}^{35} (5 i - 3)$ .

02

simplify the sum.

Express the sum and identify the values.

$\begin{array}{rcl} \sum_{i = 1}^{35} (5 i - 3) & = & (5 (1) - 3) + (5 (2) - 3) + (5 (3) - 3) + \dots + (5 (35) - 3) \\ = & 2 + 7 + 13 + \dots + 172 \\ = & a_{1} + a_{2} + a_{3} + \dots + a_{35} \end{array}$

Thus, the obtained values are $a_{1} = 2$ and $a_{35} = 172$ .

03

Step 3. Find the sum.

Substitute the values in the some formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ .

$\begin{array}{rcl} S_{35} & = & \frac{35}{2} (2 + 172) \\ = & \frac{35}{2} (174) \\ = & 35 (87) \\ = & 3045 \end{array}$

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Most popular questions from this chapter

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

$a_{1} = 8$ and $d = - 2$

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