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SeqLab
aₙ = a₁ · rⁿ⁻¹.
Where arithmetic sequences add the same amount each time, geometric sequences multiply by the same ratio r — 2, 6, 18, 54… multiplies by 3 every step, which is why growth accelerates so much faster.
Compound interest, population growth, and viral spread are all geometric processes — this is the same mathematical structure behind 'doubling every period' scenarios.
aₙ (nth term)
486
aₙ = a₁ · rⁿ⁻¹
What you entered
nth term: a₁ · rⁿ⁻¹
2 × 3^5= 486Sum of first n terms
2 × (1 − 3^6) ÷ (1 − 3)= 728Result
aₙ (nth term): 486
Starting at 2 with common ratio 3, term 6 is 486, and the first 6 terms sum to 728.