question_answer

How many terms of the A.P. 27, 24, 21,... should be taken so that their sum is zero?

Answer:

Given, A.P. is 27, 24, 21,...

We have, \[a=27,\text{ }d=24-27=21-24=-3\]

Now, \[{{S}_{n}}=0\]

Therefore,                      \[{{S}_{n}}=\frac{n}{2}[2a+(n-1)d]=0\]

\[\Rightarrow \,\frac{n}{2}[2(27)+(n-1)(-3)]=0\]

\[\Rightarrow \,54-3n+3=0\]

\[\Rightarrow \,57-3n=0\]

\[\Rightarrow \,3n=57\]

\[\therefore n=19\]

Hence, the no. of terms are 19