Find whether 55 is a term of the A.P. 7, 10, 13, …. or not. If yes find which term is it.

Here, a₂ - a₁ = 10 - 7 = 3,     a₃ - a₂ = 13 - 10 = 3,

i.e. any term - preceding term = 3, a fixed number.
So, the given list of numbers forms an A.P. with a = 7 and d = 3.

Now we want to find whether there exists a natural number n for which a_n = 55

⇒ a + (n - 1)d = 55
⇒ 7 + (n - 1)3 = 55
⇒ 7 + 3n - 3 = 55
⇒ 4 + 3n = 55
⇒ 3n = 51
⇒ n = 17.

Hence, 55 is the 17th term of the A.P. 7, 10, 13 …..