Find the number of terms in the following A.P.

7, 13, 19, …, 205

The first term, a = 7

Common difference, d = a₂ − a₁ = 13 − 7 = 6

Let there are n terms in this A.P.

a_n = 205

As we know, for an A.P.,

a_n = a + (n − 1) d

Therefore, 205 = 7 + (n − 1) 6

198 = (n − 1) 6

33 = (n − 1)

n = 34

Therefore, this given series has 34 terms in it.