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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 71-82, find the sum of each sequence.

$\sum_{k = 1}^{40} 8$

A pond currently has 2000 trout in it. A fish hatchery decides to add an additional 20 trout each month. In addition, it is known that the trout population is growing 3% per month. The size of the population after n months is given by the recursively defined sequence.

$p_{0} = 2000; p_{n} = 1.03 p_{n - 1} + 20$

(a) How many trout are in the pond at the end of the second month? That is, what is p₂?

(b) Using a graphing utility, determine how long it will be

before the trout population reaches 5000.

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

$2, - 4, 6, - 8, 10, . . .$

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$\sum_{k = 1}^{\infty} 6 {(- \frac{2}{3})}^{k - 1}$

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

${\sum (5}_{k = 1}^{20} k + 3)$

See all solutions

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