Question

If the fourth terms of an



a.P is 11 and the sum of the fourth and fifth terms is 25 find the common difference of the



a.P.

Answer 1

Solution:-

Given:-

Fourth term of an AP is 11

a(4) = 11

Sum of fourth and fifth term of an AP is 25

a(4) + a(5) = 25

_______________________

a(4) = 11

a + 3d = 11....(1)

a(4) + a(5) = 25

a + 3d + a + 4d = 25

2a + 7d = 25.....(2)

From equation (1) and (2) we get. .

a + 3d = 11

2a + 7d = 25

Multiply equation (1) by 7 and (2) by 3 then we get ..

(a + 3d = 11 ) × 7.

7a + 21d = 77.....(3)

(2a + 7d = 25 ) × 3

6a + 21d = 75....(4)

From equation 3 and 4 we get...

a = 2

Put the value of a in equation 1...

a + 3d = 11

2 + 3d = 11

3d = 11 - 2

3d = 9

d = 9/3

d = 3

So, the common difference of an AP is 3