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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: Q. 39 (page 816)

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

Short Answer

Expert verified

The sum of the given sequence is $\frac{9 n + 5 n^{2}}{2}$ .

Step by step solution

Step 1. Given information

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

We have to find the sum of the sequence.

Step 2. calculating the sum

$\begin{array}{l} Thesumofthearithmeticsequenceisgivenas \\ 鈬� S_{n} = \frac{n (a_{1} + a_{n})}{2} \\ Wehave, \\ a_{1} = 7 \\ a_{n} = 2 + 5 n \\ Thus, \\ 鈬� S_{n} = \frac{n (7 + (2 + 5 n))}{2} \\ = \frac{n (9 + 5 n)}{2} \\ = \frac{9 n + 5 n^{2}}{2} \end{array}$

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Find each sum.7+12+17+...+2+5n

Short Answer

Step by step solution

Step 1. Given information

Step 2. calculating the sum

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