Posted by bill on Sunday, March 7, 2010 at 9:41pm.
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.
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?

math  Reiny, Sunday, March 7, 2010 at 11:18pm
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)