Algebra
Class 11

Geometric Progression - nth Term

an=arn1a_n = a \cdot r^{n-1}
24681002004006008001000
aₙ = a × r^(n-1)

Adjust Variables

First term (a)
a =
1100
Common ratio (r)
r =
0.13

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.

Real-World Applications

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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