Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example.

Question

Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example.

Answer 1

The sum S of an arithmetic series, starting at a, with difference d, and having n terms is given by first term plus last term times number of terms divided by 2

S=n(a+a+(n-1)d)/2

If this sum is to be zero then we need 0=n(a+a+(n-1)d)/2 or

0=n(a+a+(n-1)d) or, assuming there are n>0 terms

0=2a+(n-1)d.  Now you can play.

let a=-5, n=6, and have 0=-10+5d or d=2

-5, -3, -1, 1, 3, 5 sum 0.  Create your own examples.