if the sum of m terms of an ap to the sum of n terms of another ap is m2 to n2 (ratio),show that mth term to nth term is 2m-1 to 2n-1...

Let a and b be the first term and the common difference of the A.P. respectively.

According to the given condition,

Putting m = 2m – 1 and n = 2n – 1 in (1), we obtain

From (2) and (3), we obtain

Thus, the given result is proved.