There are $$3$$ positive real numbers. The second is greater than the first by the same amount that the third is greater than the second. The product of the two smaller numbers is $$85$$ and that of the two bigger numbers is $$115$$. Then the difference between the smallest and the greatest numbers is

Let the three numbers in arithmetic progression be $$u-d,u,u+d$$. Dividing the two product equations gives $$\frac{u+d}{u-d}=\frac{115}{85}=\frac{23}{17}$$, so the numbers may be written as $$17k,20k,23k$$. Since $$17k \times 20k=85$$, we get $$k=\frac{1}{2}$$. The required difference is $$23k-17k=6k=3$$.