Question

Find the number of terms in the following A.P.: 7, 13, 19, ..., 205.

How many terms are there in the A.P.?

7, 13, 19, ..., 205.

Answer 1

For this A.P.,

a = 7

d = a₂ − a₁ = 13 − 7 = 6

Let there are n terms in this A.P.

a_n = 205

We know that

a_n = a + (n - 1) (d)

⇒ 205 = 7 + (n - 1) (6)

⇒ 205 = 7 + 6n - 6

⇒ 6n = 205 + 6 - 7

⇒ 6n = 204

⇒ n = `204/6`

⇒ n = 34

Thus, the required number of terms is 34.