nth term, partial sums and term lists for geometric sequences.
Input
Answer
Steps
Why it works
Each term multiplies by r, so aₙ = a₁·rⁿ⁻¹. For the sum, Sₙ − rSₙ telescopes: every middle term cancels, leaving Sₙ = a₁(rⁿ−1)/(r−1) — the engine behind compound interest and infinite series.
