# 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

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