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How to Find a Ratio of a Fibonacci Sequence

The Fibonacci sequence is a series of numbers discovered by Leonardo Fibonacci in the 12th century. Dividing any term in the sequence by the previous term generates an approximation of the golden ratio, or Phi, which is 1.618 rounded to three decimals places. Using the first several terms in the sequence to generate the ratio gives a different ratio, but using successively higher terms generates a ratio that converges on, or gets closer to, Phi. After the 40th term, Phi is accurate to 15 decimal places. Phi and its reciprocal, 0.618, are found throughout nature in certain plants and animals and in ancient architecture, such as the Egyptian pyramids.

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Instructions

- 1
  Write the first two terms of the Fibonacci sequence, which are 0 and 1.
- 2
  Calculate the third through 15th terms in the Fibonacci sequence by adding the last number in the sequence to the previous number in the sequence. For example, 1 plus 0 equals 1, which is the third term. 1 plus 1 equals 2, which is the fourth term. The first 15 terms are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and 377.
- 3
  Divide any term in the sequence that is the 11th term or higher by the previous term in the sequence to calculate the ratio 1.618. For example, divide the 11th term, which is 55, by the 10th term, which is 34, to get 1.61798, which rounds to 1.618; 55 divided by 34 also equals 1.61798, or 1.618.
- 4
  Divide any term in the sequence that is the ninth term or higher by the next term in the sequence to calculate the ratio 0.618. For example, divide the ninth term, which is 21, by the 10th term, which is 34, to get 0.6176, which rounds to 0.618; 21 divided by 34 also equals 0.6176, or 0.618.

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