In the A.P. 8, 13, 18, ……., the n^th term is 83, then n is equal to :

1. 14

2. 16

3. 13

4. 15

In the A.P.,

First term (a) = 8

Common difference (d) = 13 - 8 = 5.

By formula,

⇒ a_n = a + (n - 1)d

Substituting values we get :

⇒ 83 = 8 + 5(n - 1)

⇒ 83 = 8 + 5n - 5

⇒ 83 = 5n + 3

⇒ 83 - 3 = 5n

⇒ 80 = 5n

⇒ n = $\dfrac{80}{5}$ = 16.

Hence, Option 2 is the correct option.