It is a very well known mathematical fact that the limiting ratio of consecutive terms of the Fibonacci sequence [F
_{0}=0, F
_{1}=1, F
_{n}=F
_{n1}+F
_{n2}] is Ļ=(1+ā5)/2 as nāā.
Suppose we generalize the definition of the sequence to:
F_{n}=AF_{n1}+BF_{n2}.
Find an expression for the limiting ratio of consecutive terms (in terms of A and B.)
Find formulas for A and B to make the limiting ratio any whole number N.
(In reply to
re: solution by Steve Herman)
a) I did substitute A=1, and show that formula in the middle of the post, with a table of B values to be used for A=1 when N is anywhere from 1 to 10.
b) I took limiting ratio to mean an asymptotic approach, rather than just ask for a geometric sequence.
c) Agreed.

Posted by Charlie
on 20151207 19:54:13 