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, 4, 5 and 6.

               $=[-2 (3)+5] +[ -2 (4) +5]+[-2 (5)+5]+[-2 (6)+5]$

               $=[-6+5] +[ -8 +5]+[-10+5]+[-12+5]$

               $=[-1] +[ -3]+[-5]+[-7]$

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.