It is a very well known mathematical fact that the limiting ratio of consecutive terms of the Fibonacci sequence [F0
] is φ=(1+√5)/2 as n→∞.
Suppose we generalize the definition of the sequence to:
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.
Posted by Charlie
on 2015-12-07 19:54:13