Question

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

Answer 1

Given that AP 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,

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

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

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

$\Rightarrow n=0and57-3n=0$

$\Rightarrow 57=3n$

$\therefore n=0andn=19$

Since the number of terms cannot be equal to 0, so n = 19