11. Another sequence closely related to the Fibonacci sequence is the Lucas sequence, which is formed using the same recursive rule but different starting numbers. The th Lucas number is given by
Calculate the ratio of successive terms of the Lucas sequence:
What do you notice?
11.
(a) 4, 7, 11, 18, 29, 47, 76, 123
(b) 3, 1.333, 1.75, 1.571, 1.636, 1.611, 1.621, 1.617, 1.618. The ratios approach .