# Geometric sequence from integer and decimal parts

A positive number has a decimal part and an integer part. The decimal part, the integer part, and the positive number itself form a geometric sequence. Find this positive number.

My attempt: Let...

• d=decimal part
• i=integer part
• e=the entire number
Then $\frac{d}{i}=\frac{i}{e}$. I also noticed $e=i+d$ so $\frac{d}{i}=\frac{i}{d+i}$. But there are still too many variables and it seems I don't have enough information to solve this.