In a geometric progression, the fourth term exceeds the third term by $$24$$ and the sum of the second and third term is $$6$$. Then, the sum of the second, third and fourth terms is ------.

With first term $$a$$ and common ratio $$r$$, the conditions give $$ar^2(r-1)=24$$ and $$ar(1+r)=6$$, which combine to $$r^2-5r-4=0$$, so $$r=\frac{5+\sqrt{41}}{2}$$ for the increasing case. Solving for $$a$$ and computing $$ar+ar^2+ar^3$$ with this ratio gives a sum of approximately $$35.1$$.