Question

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

Answer 1

Sn=n/2{2a+(n-1)d}
here a=18
d=-2
Sn=0(because it has asked how many terms must be taken to give sum =0)
➡0=n/2{2×18+(n-1)-2}
➡0=n/2{36-2n+2}
➡0=36n-2n^2+2n
➡0=38n-2n^2
➡2n^2-38n=0
Divide this equation by 2
we get➡n^2-19n
➡n(n-19)=0
➡either 'n'=0 or 'n-19'=0
➡n=0 or n=19
since number of terms can not be zero therefore we discard n=0
and the sum of 19th term will give the sum 0