Here, a = 21, d = 18 – 21 = – 3 and an = – 81, and we have to find n.
As an = a + ( n – 1) d,
we have – 81 = 21 + (n – 1)(– 3)
– 81 = 24 – 3n
– 105 = – 3n
So, n = 35
Therefore, the 35th term of the given AP is – 81.
Next, we want to know if there is any n for which an = 0. If such an n is there, then
21 + (n – 1) (–3) = 0,
i.e., 3(n – 1) = 21
i.e., n = 8
So, the eighth term is 0.