Two A.P.'s have same common difference. If the difference between their 25^th terms is 8, the difference between their 50^th terms is :

1. 16

2. 5

3. 8

4. 25

Let two A.P.'s have first term a₁ and a₂.

Their common difference be d.

By formula,

⇒ a_n = a + (n - 1)d

25th term of first A.P. = a₁ + (25 - 1)d = a₁ + 24d.

25th term of second A.P. = a₂ + (25 - 1)d = a₂ + 24d.

Given, Difference between 25th terms is 8.

∴ (a₁ + 24d) - (a₂ + 24d) = 8

a₁ - a₂ + 24d - 24d = 8

a₁ - a₂ = 8.

50th term of first A.P. = a₁ + (50 - 1)d = a₁ + 49d.

50th term of second A.P. = a₂ + (50 - 1)d = a₂ + 49d.

Difference = (a₁ + 49d) - (a₂ + 49d) = a₁ - a₂ = 8.

Hence, Option 3 is the correct option.