Sunday, February 27, 2011

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.

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