• # question_answer 1) How many terms of the A.P. 27, 24, 21,... should be taken so that their sum is zero?

 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