Question

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

Answer 1

sum of AP = n/2{2a+(n-1)d} =0.
where a= first term , d=common diff , n =numbers of term.
now it gives (n-1)d = -2a.
infinite numbers of values of n,d , and a satisfy the equation so infinite no of series can be found...
for examle put n=10 ,d=2 then a=-9..
then the series.....-9,-7,-5,-3 ............
in similar manner you can get infinite no of series by putting different
values of a, n n and d which satisfy the equation..