Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of `7^(t h)`and `(m-1)^(t h)`numbers is 5 : 9. Find the value of m.

Explanation

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Understand the Problem
We are given that there are \( m \) numbers inserted between 1 and 31 such that the resulting sequence forms an Arithmetic Progression (AP). The ratio of the 7th term to the \( (m-1) \)th term is given as \( 5:9 \).

### Step 2: Determine the Total Number of Terms
Since there are \( m \) numbers inserted between 1 and 31, the total number of terms in the sequence will be \( m + 2 \) (including 1 and 31).

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