Q. 123.9( 165 Votes )

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

Answer :

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

Given,

Sum of m terms of A.P. = S_{m}

Sum of n terms of A.P. = S_{n}

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

⇒

∴ Ratio of m^{th} and n^{th} term is (2m – 1) : (2n – 1).

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