Chapter 12: Q. 51 (page 817)

In Problems 37–54, find each sum.
$\sum_{n = 1}^{100} (6 - \frac{1}{2} n)$

Short Answer

Expert verified

$\sum_{n = 1}^{100} (6 - \frac{1}{2} n) = - 1925$

Step by step solution

Given Information

$\sum_{n = 1}^{100} (6 - \frac{1}{2} n)$

first term

use the given sum to find out the first term a1

$\sum_{n = 1}^{100} (6 - \frac{1}{2} n) a_{n} = (6 - \frac{1}{2} n) T o f i n d a_{1}, s u b s t i t u t e n = 1 a_{1} = (6 - \frac{1}{2} (1)) = \frac{11}{2}$

find out last term

To find out last term , we substitute n=100

$a_{n} = (6 - \frac{1}{2} n) a_{100} = (6 - \frac{1}{2} (100)) = - 44$

Sum

To find out sum we use sum formula

$S_{n} = \frac{n}{2} (a_{1} + a_{100}) S u m o f 100 t e r m s S_{100} = \frac{100}{2} (\frac{11}{2} + - 44) S_{100} = 50 (\frac{11}{2} - \frac{88}{2}) S_{100} = 25 (- 77) S_{100} = - 1925$

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In Problems 37–54, find each sum.
$\sum_{n = 1}^{100} (6 - \frac{1}{2} n)$

Short Answer

Step by step solution

Given Information

first term

find out last term

Sum

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In Problems 37–54, find each sum.∑n=1100(6-12n)

Short Answer

Step by step solution

Given Information

first term

find out last term

Sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 37–54, find each sum.
$\sum_{n = 1}^{100} (6 - \frac{1}{2} n)$