Which term of the AP: 21, 18, 15, ... is -81? Also, is 0 a term of this AP? Give reasons for your answer.                                                                                                                                                                                                                                   [Page No. 185]

Here, $a = 21$, $d = -3$

$$n^{\text{th}} \text{ term: } a_n = 21 + (n - 1)(-3)$$

For $-81$, $$21-3(n-1)=-81$$

$$21 - 3n + 3 = -81$$

$$24 - 3n = -81$$

$$-3n = -105$$

$$n = 35$$

So, $-81$ is the $35^{\text{th}}$ term.

Now check whether 0 is a term:

$$21 - 3(n - 1) = 0$$

$$24 - 3n = 0$$

$$3n = 24$$

$$n = 8$$

So, $8^{\text{th}}$ term of this A.P. is 0.