How many terms of the A.P. 27, 24, 21, ... are required to get the sum as 0?
19
Given that the A.P. is 27, 24, 21 …
a=27;d=24−27=−3
Sn=n2(2a+(n−1)d)
Since the sum is 0
⇒n2[2×27+(n−1)(−3)]=0
⇒ n(54−3n+3)=0
⇒ n(57−3n)=0
⇒n=0 or 57−3n=0
∴n=0 or n=19
Since the number of terms cannot be equal to 0, we have n=19.