SOLUTION: Consider the sequence that begins 4, 3, ... and continues by the rule: Every subsequent element of the sequence is the sum of the two preceding elements. a. Determine the next f

Algebra ->  Sequences-and-series -> SOLUTION: Consider the sequence that begins 4, 3, ... and continues by the rule: Every subsequent element of the sequence is the sum of the two preceding elements. a. Determine the next f      Log On


   

Question 56303This question is from textbook
: Consider the sequence that begins 4, 3, ... and continues by the rule: Every subsequent element of the sequence is the sum of the two preceding elements.
a. Determine the next five (third through seventh) elements of this sequence.
b. Compute the ratio of the sixth and seventh elements of this sequence. Is it close to the Golden Ratio? This question is from textbook

Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
So your pattern would be ...
a + b = c .... b + c = d .... c + d = e .... and so on
4, 3, 7, 10, 17, 27, 44 ....
27/44 is the ratio of the 6th and 7th terms.
The golden ratio is approx 1.618 .....
so the ratio of the 6th to 7th is NOT close to the golden ration ...
the ratio of the 7th to the 6th .... 44/27 IS close to the golden ratio.