The Fibonacci sequence of numbers begins 1,1,2,3,5,8,13,21,34,55,…and continues by the rule: every number is the sum of the two previous numbers.

Question

a. Determine the next five (eleventh through fifteenth) elements of this sequence.
b. Compute the ratio of the fourteenth and fifteenth elements of this sequence. Is it close to the golden ratio?

Answer 1

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610, ...

ratio of 15th/14th = 610/377 = 1.618037

the golden ratio = (1 + √5)/2 = 1.618033989..

for a difference of .0000031
(not bad)