Question

What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum.

Answer 1

Given:

$\sum_{k=3}^{6}(-2 k+5)$

To find:

The sum of the series.

Solution:

$\sum_{k=3}^{6}(-2 k+5)$

Substitute k = 3.

$-2 (3)+5=-6+5=-1$

Substitute k = 4.

$-2 (4)+5=-8+5=-3$

Substitute k = 5.

$-2 (5)+5=-10+5=-5$

Substitute k = 6.

$-2 (6)+5=-12+5=-7$

$\sum_{k=3}^{6}(-2 k+5)=(-1)+(-3)+(-5)+(-7)$

Apply minus plus rule: $+(-a)=-a$

                    $=-1-3-5-7$

                    $=-16$

$\sum_{k=3}^{6}-2 k+5=-16$

Therefore the sum of the series is -16.