Let \(P, Q, R\) and \(S\) be the sum of \(n\) terms, \(2n\) terms, \(3n\) terms and \(4n\) terms respectively of an AP such that \(Q=3P\). Which one of the following is correct?
\(5R=3S\)
With first term \(a\) and common difference \(d\), the condition \(Q=3P\) gives \(2a=(n+1)d\). Substituting into \(R=S_{3n}\) and \(S=S_{4n}\) gives \(R=6n^2d\) and \(S=10n^2d\), so \(R/S=3/5\), i.e. \(5R=3S\).
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