#1061 · Algebra · Sequences & series

Nth term from quadratic sum

If the sum of the first $n$ terms of a series is $S_{n} = a + bn + c n^{2}$ , find an expression for the $n^{th}$ term and describe the nature of the series.

~6 minProof · checked by AISummationArithmetic progression

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VI. Harmonical Progression, Examples VI.a, No. 18

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.