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 an AP.

a_n = a + (n – 1)d

a₄ = a + (4 – 1)d = a + 3d

a + 3d = 11 ………(1)

Now, a₅ = a + 4d and a₇ = a + 6d

Now, a₅ + a₇ 

= a + 4d + a + 6d 

= 2a + 10d

2a + 10d = 34

a + 5d = 17 ……..(2)

Subtracting (1) from (2), we get

2d = 17 – 11 = 6

d = 3

The common difference = 3