if `(m+1)th, (n+1)th and (r+1)th` term of an AP are in GP.and m, n and r in HP. . find the ratio of first term of A.P to its common difference

Explanation

To solve the problem step-by-step, we will use the properties of arithmetic progression (AP) and geometric progression (GP), along with the relationship between the terms in harmonic progression (HP).

### Step 1: Identify the terms in AP
The terms given are:
- \((m+1)\)th term: \(T_{m+1} = a + md\)
- \((n+1)\)th term: \(T_{n+1} = a + nd\)
- \((r+1)\)th term: \(T_{r+1} = a + rd\)

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