Is 51 a term of the A.P. 5, 8, 11, 14, ...?

AP = 5, 8, 11, 14, …

Here, a = 5 and d = 8 – 5 = 3

Let 51 be a term, say, nth term of this AP.

We know that

a_n = a + (n – 1)d

So, 51 = 5 + (n – 1)(3)

⇒ 51 = 5 + 3n – 3

⇒ 51 = 2 + 3n

⇒ 51 – 2 = 3n

⇒ 49 = 3n

But n should be a positive integer because n is the number of terms. So, 51 is not a term of this given AP.