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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: 39 (page 816)

Find each sum
$7 + 12 + 17 + . . . . . + (2 + 5 n)$

Short Answer

Expert verified

The solution is $S_{n} = \frac{n}{2} (9 + 5 n)$

Step by step solution

01

Given information

$7 + 12 + 17 + . . . . . + (2 + 5 n)$

02

Calculation

We have, $7 + 12 + 17 + . . . . . + (2 + 5 n)$

So , $a_{1} = 7, d = 5, a_{n} = 2 + 5 n$

Now use formula,

$S_{n} = \frac{n}{2} (a_{1} + a_{n}) = \frac{n}{2} (7 + 2 + 5 n) = \frac{n}{2} (9 + 5 n)$

The sum is $S_{n} = \frac{n}{2} (9 + 5 n)$

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Most popular questions from this chapter

In Problems 11鈥�16, evaluate each factorial expression.

$\frac{5! 8!}{3!}$

In Problems 51鈥�60, write out each sum.

${鈭�}_{k = 1}^{n} {(k + 1)}^{2}$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{s_{n}\} = \{{(\frac{4}{3})}^{n}\}$

In Problems 11鈥�16, evaluate each factorial expression.

$\frac{12!}{10!}$

In Problems 71-82, find the sum of each sequence.

${鈭� (-}_{k = 1}^{24} k)$

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