Which term of the AP: 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer.

Solution

Given AP: 21, 18, 15,…
Here, a = 21,
d = 18 – 21 = –3
Let nth term of the given AP is -81.
So, an = –81
As we know,
an = a + ( n – 1) d
Thus,
– 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
⇒ 3(n – 1) = 21
⇒ n – 1 = 7
⇒ n = 8
Therefore, the eighth term is 0.