Chapter 12: Q. 15 (page 838)

In Problems 13–16, find each sum.
$\sum_{k = 1}^{40} (- 2 k + 8)$

Short Answer

Expert verified

The sum is -1320.

Step by step solution

Step 1. Given information.

The summation notation of the sequence is: $\sum_{k = 1}^{40} (- 2 k + 8)$

Step 2. Expand the summation and apply property of summation.

By using property of summation we can write:

\sum_{k = 1}^{40} (- 2 k + 8) = \sum_{k = 1}^{40} (- 2 k) + \sum_{k = 1}^{40} 8 = {- 2 \sum k}_{k = 1}^{40} + \sum_{k = 1}^{40} 8

Step 3. Apply formula of sum of n natural number.

$- 2 \sum_{k = 1}^{40} k + \sum_{k = 1}^{40} 8 = - 2 \frac{40 (40 + 1)}{2} + 8 \times 40 = - 40 \times 41 + 8 \times 40 = 40 (- 41 + 8) = - 40 \times 33 = - 1320$

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In Problems 13–16, find each sum.
$\sum_{k = 1}^{40} (- 2 k + 8)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the summation and apply property of summation.

Step 3. Apply formula of sum of n natural number.

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In Problems 13–16, find each sum. ∑k=140-2k+8

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the summation and apply property of summation.

Step 3. Apply formula of sum of n natural number.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Discrete Mathematics

Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 13–16, find each sum.
$\sum_{k = 1}^{40} (- 2 k + 8)$