Find the first term of a HP whpse secpmd ter, os `(5)/(4)` and the third term is `(1)/(2)`.

Explanation

To find the first term of a Harmonic Progression (HP) where the second term is \( \frac{5}{4} \) and the third term is \( \frac{1}{2} \), we can follow these steps:

### Step 1: Understand the relationship between HP and AP
In a Harmonic Progression, the reciprocals of the terms form an Arithmetic Progression (AP). Therefore, if the terms of the HP are \( A, \frac{5}{4}, \frac{1}{2} \), then the corresponding terms in AP will be \( \frac{1}{A}, \frac{4}{5}, 2 \).

### Step 2: Set up the equation for AP
For the terms \( \frac{1}{A}, \frac{4}{5}, 2 \) to be in AP, the difference between the second and first term should equal the difference between the third and second term:
\[
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