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

A. 5

B. 6

C. 4

D. 3

E. 7

**Answer: Option C **

__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

Related Questions on Progressions

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

A. 5

B. 6

C. 4

D. 3

E. 7

**The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
**

A. 600

B. 765

C. 640

D. 680

E. 690

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