Let ‘a’ be the first term and d be the common difference of A.P.
Using the given information, we have
⇒ 2an + (mn – n)d = 2am + (mn – m)d
⇒ 2an – 2am = (mn – m – mn + n)d
⇒ 2a(n – m) = (n – m)d ⇒ d = 2a, [n – m ≠ 0, as n ≠ m]
Now,
Hence, the required ratio is (2m – 1) : (2n – 1)