Find the first term of an AP whose 8^th and 12^th terms are respectively 39 and 59.

Solution (By Examveda Team)

1^st Method:
8^th term = a + 7d = 39 ........... (i)
12^th term = a + 11d = 59 ........... (ii)
(i) - (ii);

Or, a + 7d - a - 11d = 39 - 59
Or, 4d = 20
Or, d = 5
Hence, a + 7 × 5 = 39
Thus, a = 39 - 35 = 4
2^nd Method (Thought Process):
8^th term = 39
And, 12^th term = 59
Here, we see that 20 is added to 8^th term 39 to get 12^th term 59 i.e. 4 times the common difference is added to 39
So, CD = $$\frac{{20}}{4}$$  = 5
Hence, 7 times CD is added to 1^st term to get 39. That means 4 is the 1^st term of the AP