The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.

Let a be the first term and d be the common difference.

Given: a₄ = 11

a₅ + a₇ = 34

To find: common difference = d

Now, Consider a₄ = 11

⇒ a + (4 - 1)d = 11

⇒ a + 3d = 11 ………….(1)

Consider a₅ + a₇ = 34

⇒ a + (5 - 1)d + a + (7 - 1)d = 34

⇒ 2a + 10d = 34

⇒ a + 5d = 17 ……..(2)

Subtracting equation (1) from equation (2), we get,

2d = 6

⇒ d = 3

∴ Common difference = d = 3