Question

Find how many terms of the following series are needed to make the given sum:
64+62+60...=0

Answer 1

The sum of a series is calculated with the following formula:
n/2(2a+(n-1)d) where n is the number of terms, a is the first term and d is the difference between the terms.

so for this series:
n/2(2*64+(n-1)*-2)=0
n(130-2n)=0
n=0 (not valid because n<1) n=65
so the 65th term gives the sum 0