The sum of the first \(n\) terms of an A.P. is \(S_n = 3n^2 + 5n\). Find the A.P. and its \(n\)th term.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: A.P. 8, 14, 20, …; \(t_n = 6n + 2\)

\(t_1 = S_1 = 3 + 5 = 8\)

\(S_2 = 12 + 10 = 22 \Rightarrow t_2 = S_2 - S_1 = 22 - 8 = 14\)

\(d = 14 - 8 = 6\). The A.P. is 8, 14, 20, 26, …

\(t_n = a + (n - 1)d = 8 + 6(n - 1) = 6n + 2\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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