A sequence of numbers similar to the Fibonacci sequence, called the Lucas sequence, uses the same recursion rule but different starting numbers. The rule for the Lucas sequence is Ln = Ln-1 + Ln-2 where L1 = 1 and L2 = 3.
a. Given that L2 = 3, find the next 10 values of the Lucas sequence by using the numbers in the Fibonacci sequence according to the recursion rule Ln = fn+1 + fn-1.
b. For the Fibonacci sequence defined by the recursion rule fn = fn-1 + fn-2 with f1 = 1 and f2 = 1 and the Lucas sequence defined by the recursion rule Ln = Ln-1 + Ln-2 with L1 = 1 and L2 = 3, complete the following table. What do you notice about the numbers in the last two columns?
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