Question

Help please what is the sum of the series ?

Answer 1

Comment
There are 4 terms in this series
That's because the summation (Sigma) goes from 3 to 6 inclusive. So k takes on values of  3,4,5,6

You could use this summation formula

Formula 
Sum = (a + L)n/2

Substitution 
a is the first term.
k = 3 for the first term
a = -5k + 20
a = -5(3) + 20
a = -15 + 20
a = 5

For the last term k = 6
L = -5(6) + 20
L = -30 + 20
L = - 10

Sum
Sum = (5 - 10)*4/2
Sum = -5 * 2
Sum = -10

Comment
You may wonder how come the last term and the sum are the same. The reason to be found by figuring out the 4 terms and adding them together.

When k = 3, -5k + 20 = -15 + 20 = 5
When k = 4, -5k + 20 = -20 + 20 = 0
When k = 5, -5k + 20 = -25 + 20 = -5
When k = 6, -5k + 20 = -30 + 20 = -10

Sum = 5 + 0  - 5 - 10 = - 10

Conclusion. 
It is an accident of the numbers.

Answer: - 10 = the Sum