The sum of the 2nd and 5th terms of and A. P is 42.if the difference between the 6th and the 3rd is 12. Find the a. Common difference ?

Let the first term of the A.P be a and the common difference be d.

The 2nd term = a + d
The 5th term = a + 4d
The 6th term = a + 5d
The 3rd term = a + 2d

Given that the sum of the 2nd and 5th terms is 42:
(a + d) + (a + 4d) = 42
2a + 5d = 42

Given that the difference between the 6th and the 3rd terms is 12:
(a + 5d) - (a + 2d) = 12
3d = 12
d = 4

Substitute d = 4 into the first equation:
2a + 5(4) = 42
2a + 20 = 42
2a = 22
a = 11

Therefore, the common difference of the A.P is 4.