Question

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.

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

a₄ = 11

⇒ a + (4 – 1)d = 11   ...[a_n = a + (n – 1)d]

⇒ a + 3d = 11   ...(1)

Now, 

a₅ + a₇ = 34   ...(Given) 

⇒ (a + 4d) + (a + 6d) = 34 

⇒ 2a + 10d = 34 

⇒ a + 5d = 17   ...(2)

From (1) and (2), we get

11 – 3d + 5d = 17

⇒ 2d = 17 – 11 = 6

⇒ d = 3

Hence, the common difference of the AP is 3.