Question

The product of three no. In ap is 224 and largest no. Is 7 times the smallest . Find the no.

Answer 1

let the numbers be 
a-d, a , a+d 
a(a^2-d^2) =224 
a+d = 7(a-d) 
a+d = 7a-7d
6a=8d
a=8d/6 = 4d/3 


a(a^2-d^2) =224
4d/3((4d/3)^2 -d^2)=224
d(16d^2/9 -d^2) =56*3 
d(16d^2-9d^2)/9)=56*3 
d(7d^2) = 56*3*9 
7d^3= 56*3*9/7 
d^3= 8*3*9 
d=6
a=8 
the numbers 2,8,14

Hope it helps