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if the A.M. between pth and qth terms of...

if the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., then show that `p+q=r+s`

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To prove that if the A.M. between the p-th and q-th terms of an A.P. is equal to the A.M. between the r-th and s-th terms of the A.P., then \( p + q = r + s \), we can follow these steps: ### Step 1: Write the formula for the n-th term of an A.P. The n-th term of an A.P. can be expressed as: \[ a_n = a + (n - 1)d \] where \( a \) is the first term and \( d \) is the common difference. ...
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