Let the required parts be (a -3d) , (a -d) , (a+d) and ( a+3d)
then , ( a-3d) + ( a-d) + (a+d) + ( a+3d) = 32 ` Rightarrow 4a = 32 Rightarrow a=8`
So, the required parts are ( 8-3d) , ( 8-d) , ( 8+d) and ( 8 +3d)
But product of extermes is to the product of means as 7:15
`((8-3d)(8+3d))/((8-d)(8+d)) =7/15`
`((64-9d^(2)))/((64-d^(2)))=7/15`
`Rightarrow 15( 64-9d^(2)) Rightarrow d^(2) = 512/128=4 Rightarrow d = +-2`
Thus, ( a=8 and d=2) or (a =8 and d =-2)
Hence, the required parts are 2,6,10,14,or 14, 10,6,2
