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).

Question

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).

Philoid · Accepted 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).

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).