Question

Find whether 0 (zero) is a term of the A.P. 40, 37, 34, 31,... .

 

Answer 1

Let a be the first term and d be the common difference.

We know that, n^th term = a_n = a + (n − 1)d

It is given that a = 40, d = −3 and a_n = 0

According to the question,

⇒ 0 = 40 + (n − 1)(−3)

⇒ 0 = 40 − 3n + 3

⇒ 3n = 43

⇒ n =  \[\frac{43}{3}\]        ....(1)

Here, n is the number of terms, so must be an integer.

Thus, there is no term where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ... .