Question

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

Answer 1

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

First term, a = 21

Common difference, d = 18 − 21 = −3

Suppose n^th term of the given AP is −81. Then,

$$\begin{gathered} a_n=-81 \\ \Rightarrow 21+\left(n-1\right)\times \left(-3\right)=-81\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow -3\left(n-1\right)=-81-21=-102 \\ \Rightarrow n-1=\frac{102}{3}=34 \end{gathered}$$
$\Rightarrow n=34+1=35$

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