Question

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

Answer 1

AP is $21,18,15,...$

$a=21$,

$d=18-21=-3$

Sum of terms $=S_n=0$

$\frac{n}{2}[2a+(n-1\left)d\right]=0$

$\frac{n}{2}\left[2\right(21)+(n-1\left)d\right]=0$

$\frac{n}{2}[45-3n]=0$

$[45-3n]=0$

$n=15$ (number of terms)

Thus, $15$ terms of the given AP sums to zero.