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Chapter 12: 46 (page 816)

Find each sum
$7 + 1 - 5 - 11 - . . . . . - 299$

Short Answer

Expert verified

The solution is $S_{52} = - 7592$

Step by step solution

01

Given information

$7 + 1 - 5 - 11 - . . . . . - 299$

02

Calculation

We have, $7 + 1 - 5 - 11 - . . . . . - 299$

So, $a_{1} = 7, d = - 6, a_{n} = - 299$

Now use formula

$a_{n} = a_{1} + (n - 1) d \Rightarrow - 299 = 7 + (n - 1) (- 6) \Rightarrow - 299 = 7 - 6 n + 6 \Rightarrow - 6 n = - 312 \Rightarrow n = 52$

To find sum $S_{52}$

role="math" localid="1649306434221" $S_{52} = \frac{52}{2} [7 + (- 299)] = - 7592$

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Most popular questions from this chapter

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

$8 + 12 + 18 + 27 + . . . .$

In Problems 61–70, express each sum using summation notation.

$1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}$

Find x so that x, x + 2, and x + 3 are consecutive terms of a geometric sequence.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 1; a_{2} = 2; a_{n} = a_{n - 1} \cdot a_{n - 2}$

If $$ 1000$ is invested at $4 %$ per annum compounded semiannually, how much is in the account after 2 years?

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