Question

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

• A. 27
• B. 19
• C. 24
• D. 17

Answer 1

The correct option is B

19

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

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

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

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

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

$\therefore n=0andn=19$

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