Question 814617
Let's develop a sequence that describes what happens
as group size increases.
For a group of 2 we get 2(2(2)), that is each of the two girls in
the group gets 2*2 oranges.
For a group of 3 we get 3(2(3)).

So a particular element of our sequence will be n(2n) were n is a positive integer.

Consider the equation n(2n) = 1250.  Solving for n should give us the group size.
n(2n) = 1250
{{{2n^2 = 1250}}}
Divide each side by 2
{{{n^2 = 625}}}
Take the square root of each side and we have
n = 25.