Question

How many terms of the A.P. 27, 24, 21, ... are required to get the sum as 0?

Answer 1

Given that the A.P. is 27, 24, 21 …
$a=27;d=24-27=-3$

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

Since the sum is 0

$\Rightarrow \frac{n}{2}[2\times 27+(n-1\left)\right(-3\left)\right]=0$

$\Rightarrow n(54-3n+3)=0$

$\Rightarrow n(57-3n)=0$

$\Rightarrow n=0$ or $57-3n=0$

$\therefore n=0$ or $n=19$

Since the number of terms cannot be equal to 0, we have $n=19$.