Divide 56 in four parts in
a.P. Such that the ratio of the product of their extreme (1st and 4th) to the product of means (2nd and 3rd) is 5 :
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4 no =a-3d,a-d,a+d,a+3d
sum , 4a=56
a=14
(a-3d)(a+3d)/(a-d)(a+d)=5:6
6(a²-9d²)=5(a²-d²)
a²=54d² - 5d²
14² =49d²
d²=14² /7²
d=±14/7=±2
for d=2,
a-3d=14-6=8
a-d=14-2=12
a+d=14+2=16
a+3d=14+6=20
Numbers are 8,12,16,20
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