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Test: Fibonacci sequence and golden ratio

This test explores the rule of the Fibonacci sequence and ratios of consecutive terms. Tasks require students to continue the sequence, find missing terms and explain how Fibonacci numbers relate to the golden ratio.

Question qty: 10
Duration in minutes: 15
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Sample questions

  • What does it mean that a segment is divided in the golden ratio?
  • The shorter side of a golden rectangle is s cm. Approximate the longer side using 1.618.
  • A Fibonacci sequence fragment is a, b, c, ... Find the next term.
  • What is term n of 1, 1, 2, 3, 5, ...?
  • Which phrase precisely states the Fibonacci rule?
  • The longer side of a golden rectangle is l cm. Approximate the shorter side.
  • Insert the missing Fibonacci term: a, X, c.
  • Each new term equals the sum of the previous two. They are a and b. Find the new term.

Fibonacci sequence and golden ratio

In the Fibonacci sequence, every term from the third onward is the sum of the two preceding terms: Fₙ = Fₙ₋₁ + Fₙ₋₂. Check the stated starting values and indexing convention.

The golden ratio

The golden ratio φ satisfies φ = 1 + 1/φ, giving φ = (1 + √5)/2. Ratios of consecutive Fibonacci numbers approach φ but are generally not exactly equal to it at a finite step. In geometry, match the ratio of the longer to shorter part with the ratio of the whole to the longer part.

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