# Which term of the AP 21, 18, 15, ... is −81?

Question:

Which term of the AP 21, 18, 15, ... is −81?

Solution:

The given AP is 21, 18, 15, ... .

First term, a = 21

Common difference, d = 18 − 21 = −3

Suppose nth term of the given AP is −81. Then,

$a_{n}=-81$

$\Rightarrow 21+(n-1) \times(-3)=-81 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow-3(n-1)=-81-21=-102$

$\Rightarrow n-1=\frac{102}{3}=34$

$\Rightarrow n=34+1=35$

Hence, the 35th term of the given AP is −81.