The nth term of a GP where a is first term and r is common ratio. Each term is multiplied by r to get the next.
Compound interest — Principal grows geometrically: P(1+r)ⁿ.
Bacterial growth — Population doubles every hour: P₀ × 2ⁿ.
Radioactive decay — Half-life: remaining mass = M₀ × (1/2)ⁿ.
Paper folding — Each fold doubles thickness: t × 2ⁿ.
Viral spread — Each person infects r others: infections grow as rⁿ.
Sound decibels — Loudness perception is logarithmic; actual energy is geometric.
Chess legend — Grains on chessboard: 2⁰ + 2¹ + ... + 2⁶³.
Depreciation — Car value at 15% depreciation: V₀ × 0.85ⁿ.
Drug metabolism — Drug concentration halves every period.
Social media reach — Posts shared geometrically go viral.
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