If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: Proved, \(t_{m+n} = 0\)

\[m[a + (m - 1)d] = n[a + (n - 1)d]\]\[a(m - n) + d[(m^2 - n^2) - (m - n)] = 0\]\[(m - n)[a + (m + n - 1)d] = 0\]

For \(m \neq n\): \(a + (m + n - 1)d = 0\). But \(t_{m+n} = a + (m + n - 1)d\), so \(t_{m+n} = 0\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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