Question

How many terms of $AP:27,24,21,.....$ should be taken so that their sum is zero? What is the value of that last term.

Answer 1

Let first term be $a=27$

And common difference be $d=-3$

According to question, sum is zero,

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

$⟹[54+(n-1\left)\right(-3\left)\right]=0$

$⟹n=19$

Hence, $19$ terms of AP should be taken to make sum zero.

Value of the last term, i.e;

$a_{19}=a+(19-1)d$

$⟹a_{19}=27+\left(18\right)(-3)$

$⟹a_{19}=-27$