find five number in AP whose sum is 12 1/2 and the ratio of the first to last is 2:3
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Sum of an AP is given by n/2 (2a+(n-1)d)
Siince sum of first 5 terms is given ∴ 5/2 (2a+4d)=25/2
= a+2d=5/2 ___(1)
and a/d=2/3 __(2)
∴ put value of a from (2) in (1) we get 2d/3 +2d=5/2
∴d=15/16 and a=2d/3 =5/8
therefore first five numbers are a ,a+d,a+2d,a+3d,a+4d
5/8,25/16,40/16,55/16,70/16
Siince sum of first 5 terms is given ∴ 5/2 (2a+4d)=25/2
= a+2d=5/2 ___(1)
and a/d=2/3 __(2)
∴ put value of a from (2) in (1) we get 2d/3 +2d=5/2
∴d=15/16 and a=2d/3 =5/8
therefore first five numbers are a ,a+d,a+2d,a+3d,a+4d
5/8,25/16,40/16,55/16,70/16
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