Fibonacci Type Sequence..

Question

1.) If Fsub1 and Fsub2 represent any first numbers, list the first ten terms of this Fibonacci-Type Sequence.
2.) The sixteenth Fibonacci number is 7335 and the seventeenth Fibonacci number is 11733. What is the eighteenth Fibonacci number?
2.) If Fsub23=28657 and Fsub25=75025. Find the Fsub24.

Answer 1

1) F3 =  F1+F2

F4 = F2+F3 = F2+F1+F2 =                F1+ 2F2

F5 = F3+F4 = F1+F2+2F2+F1 =      2F1+ 3F2

F6 = F4+F5 = 2F2+F1+2F1+3F2 =  3F1+ 5F2

F7 =F5+F6 = 2F1+3F2+3F1+5F2 = 5F1+ 8F2

F8 = F6+F7 =                                   8F1+13F2

F9 =                                               13F1+21F2

F10 =                                              21F1+34F2

2) 7335+11733=19068=F18 (this is not part of the "true" Fibonaccci series, where F16=987, F17=1597)

3) F23=28657, F25=75025=28657+F24, F24=75025-28657=46368

(Point of interest: the Fibonacci series is closely connected to the Golden Ratio,G=(1+√5)/2=1.618 approx. To find the next term following a given one, multiply by G and round it up to the nearest integer. The bigger the term the closer the product will be to an integer. F23=28657. F23*G=46368.00002 approx, so F24=46368 and F25=F24*G=75024.99999 approx, so F25=75025.)