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