Q12 of 97 Page 185

The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of mth and nth term is (2m – 1) : (2n – 1).

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


Given,


Sum of m terms of A.P. = Sm



Sum of n terms of A.P. = Sn






Putting m = 2m – 1 and n = 2n – 1 in the above equation





⇒


∴ Ratio of mth and nth term is (2m – 1) : (2n – 1).


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