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

A. 5

B. 6

C. 4

D. 3

E. 7

Answer: Option C

Solution(By Examveda Team)

1st Method:
8th term = a + 7d = 39 ........... (i)
12th 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
2nd Method (Thought Process):
8th term = 39
And, 12th term = 59
Here, we see that 20 is added to 8th term 39 to get 12th 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 1st term to get 39. That means 4 is the 1st term of the AP

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