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Geometric sequences: general term

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Useful for: MCR3U MCF3M IB Math AA SL & HL IB Math AI SL & HL AP® Precalculus

Learn it A geometric sequence multiplies by the same ratio r each time: tₙ = a·rⁿ⁻¹. Real examples: a ball that bounces to 80% of its height, a population that grows 5% a year.

Example: A ball dropped from 4 m bounces to 75% of its height each time. Height of the 5th bounce?

  1. a = 4 × 0.75 = 3 (first bounce), r = 0.75.
  2. t₅ = 3(0.75)⁴ ≈ 0.95 m.

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