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