What are the first term and the common difference of an A.P. if the third term is 8 and seventh term is 20 ?

The 3rd term of an AP is 8 and the 7th term of the AP is
20. Required to find the 1st term and the common ratio.

The
nth term of an AP is given by an = a1+(n-1) d, where a1 is the 1st term and d is the
common ratio.

Therefore a3 = a1 + (3-1)d =
8...(1)

a7 = a1+(7-1)d =
20...(2)

(2)- (1) gives:  (6-2) d = 20-8 =
12.

Therefore d = 12/(6-2) =
3.

Therefore  from (1), we get  a1+(3-1)d = 8. So a1 = 8-
(3-1)d = 8- 2*3 = 2.

Therefore a1 = 2 and d =
3.

Therfore the first term of the AP is a1 = 2. The common
ratio of the AP is d= 3.