# Geometric to Arithmetic Progression

Algebra Level 3

In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is $$12$$ and the last number is $$\frac{45}{2}$$. The sum of the two middle numbers can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a+b$$.

×