The sum of the 2nd and 5th terms of an A. P is 42 if the difference between the 6th and 3rd terms is 12 find the a. First term and 29th term ?

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 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 first term is 11 and the common difference is 4.

To find the 29th term:
29th term = a + 28d
29th term = 11 + 28(4)
29th term = 11 + 112
29th term = 123

Therefore, the 29th term is 123.