Geometrische Folge

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Eine Folge, bei der jedes Glied durch Multiplikation des vorherigen mit einer Konstante (Quotient) entsteht.

A geometric sequence (also called geometric progression) is a sequence where each term is obtained by multiplying the previous term by a fixed number called the 'common ratio'. Geometric sequences model exponential growth and decay, compound interest, population growth, and many natural phenomena.

aₙ = a₁ × rⁿ⁻¹, where r is the common ratio

• 2, 6, 18, 54, 162... (common ratio = ×3)
• 1000, 500, 250, 125... (common ratio = ×0.5 or ÷2)
• 1, -2, 4, -8, 16... (common ratio = ×(-2))

So erkennen Sie es

• Divide each term by the previous term
• If all ratios are the same, it's geometric
• The pattern is 'multiply by the same number each time'

Häufige Fehler

• Confusing with arithmetic sequences (add vs multiply)
• Forgetting that division is multiplication by a fraction
• Missing negative ratios that cause alternating signs

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