Problem related to Arithmetic Progression

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

Here is the step by step explanation to the A.P problem,

Solution : 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.

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