What is the sum of the arithmetic series below?

-100 + - 95 + - 90 + - 85 + ... + - 5 + 0 + 5 + ... + 85 + 90 + 95 + 100

Hello:

the common ratio is r = - 95 - (-100) = 5

the general terme is : un = u1 + (n-1) r

un = - 100 + (n-1) (5)

un = - 100 + 5n-5

un = 5n-105

The last term is : 100

un = 100

5n-105 = 100

5n = 205

n = 41 (Number of terms)

The last term is : u 41

the sum is : S = (41/2) (-100+100) = 0