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- The ratio of the sums of m and n terms of an AP is m
^{2 }: n^{2.} show that the ratio of the m^{th} and n^{th} terms is (2m-1) : (2n-1) - In an AP, the sum of first n terms is 3n
^{2}/2 + 5n/2, find its 25^{th }term.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/2 + 5n/2, find its 25^{th }term.

Let the first term and common difference of an A.P. is a, d respectively. So, sum of m and n terms of an A.P. is as,

And,

So,

Now,

Hence, ratio of mth and nth term is 2m-1 : 2n-1.

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