If three positive numbers `a,b` and c are in AP, GP and HP as well, than find their values.

Explanation

To solve the problem where three positive numbers \( a, b, \) and \( c \) are in Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP), we can follow these steps:

### Step 1: Set up the equations based on the definitions of AP, GP, and HP.
1. **AP**: For numbers to be in AP, the middle term \( b \) is the average of the other two terms:
\[ b = \frac{a + c}{2} \tag{1} \]

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