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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
**Answer: Option C**

## Show Answer

Solution(By Apex 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 = $\Large\frac{20}{4}$ = 5
Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

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

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

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

A. 600B. 765

C. 640

D. 680