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.

Sm : Sn = m2:n2 Sm : m2 = Sn : n2 = k Tm : Tn = Sm – Sm - 1 : Sn – Sn – 1 = k{m2 – (m - 1)2} : k{n2 – (n - 1)2} = 2m – 1 : 2n - 1

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The ratio of the sums of m and n terms of an A.P is m²:n². Show that the ratio of m^th and n^th term is 2m – 1: 2n – 1.

S_m : S_n = m²:n²

S_m : m²= S_n: n² = k

T_m : T_n = S_m – S_{m - 1}: S_n – S_{n – 1}

= k{m² – (m - 1)²} : k{n² – (n - 1)²}

= 2m – 1 : 2n - 1