How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
Question:

How many terms of the AP 21, 18, 15, … must be added to get the sum 0?

Solution:

The given AP is 21, 18, 15, … .

Here, a = 21 and d = 18 − 21 = −3

Let the required number of terms be n. Then,

$S_{n}=0$

$\Rightarrow \frac{n}{2}[2 \times 21+(n-1) \times(-3)]=0 \quad\left\{S_{n}=\frac{n}{2}[2 a+(n-1) d]\right\}$

$\Rightarrow \frac{n}{2}(42-3 n+3)=0$

$\Rightarrow n(45-3 n)=0$

$\Rightarrow n=0$ or $45-3 n=0$

$\Rightarrow n=0$ or $n=15$

∴ n = 15                 (Number of terms cannot be zero)

Hence, the required number of terms is 15.