Question

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

Answer 1

We know that $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{n}{2}(2\times 21+(n-1)\times 3)$

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

$=\frac{n}{2}(45-3n)$

$=\frac{45n}{2}-\frac{3n^2}{2}$

$3n^2-45n=0$

$n(3n-45)=0$

$n=0or3n-45=0$

$3n=45\Rightarrow n=15$

On solving the quadratic equation, we get n = 15 or 0.

So, 15 terms must be added to get the sum 0.