Illuminations: Golden Ratio

The Fibonacci sequence is shown below, with each term equal to the sum of the previous two terms. If you take the ratios of successive terms, you get 1, 2, 3/2, 5/3, 8/5, 13/8, and so on. But as you proceed through the sequence, these ratios get closer and closer to a fixed number, known as the Golden Ratio.

1, 1, 2, 3, 5, 8, 13, …

Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

This brainteaser was written by Derrick Niederman.

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National Council of Teachers of Mathematics

Math Topics

Patterning & Sequencing, Ratios, Rates & Percents

K-6, Middle School, High School

5th Grade, 6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade

Fibonacci Sequence, Math Puzzles

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