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.
Time left: 00:00:00
Sample questions
- A Fibonacci sequence fragment is ___, ___, ___, ... Find the next term.
- What is term ___ of 1, 1, 2, 3, 5, ...?
- Insert the missing Fibonacci term: ___, X, ___.
- The shorter side of a golden rectangle is ___ cm. Approximate the longer side using 1.618.
- The longer side of a golden rectangle is ___ cm. Approximate the shorter side.
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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