The Fibonacci sequence of numbers begins1,1,2,3,5,8,13,21,34,55... and continues

Question

The Fibonacci sequence of numbers begins1,1,2,3,5,8,13,21,34,55... and continues by rule: Everynumber is the sum of the two previous numbers. a. Determine the next five (11th thru 15th) elements ofthis sequence. b. Compute the ratio of the 14th and 15th elements ofthis sequence. Is it close to the golden ratio? The Fibonacci sequence of numbers begins1,1,2,3,5,8,13,21,34,55... and continues by rule: Everynumber is the sum of the two previous numbers. a. Determine the next five (11th thru 15th) elements ofthis sequence. b. Compute the ratio of the 14th and 15th elements ofthis sequence. Is it close to the golden ratio?

Explanation / Answer

To calculate it, simply add the previous two sequences. so 1+1=2. 1+2=3 2+3=5 3+5=8 ...etc So a. 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610. b. Ratio of 610:377 = 1.6180... which is the golden ratio. For moreinformation, visithttp://www.mathsisfun.com/numbers/golden-ratio.html Good luck.

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