Question

What is the sum of the arithmetic series below?

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

Answer 1

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