The 4th term of an AP is 11. The sum of the 5th and 7th terms of this

1.	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» 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

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»

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