A sequence of numbers similar to the Fibonacci sequence, called the Lucas sequence, uses...

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 L_n = L_n-1 + L_n-2 where L₁ = 1 and L₂ = 3.

a. Give the first 10 numbers in the Lucas sequence.

b. For the Fibonacci sequence defined by f_n = f_n-1 + f_n-2 with f₁ = 1 and f₂ = 1, and the Lucas sequence defined by the recursion rule L_n = L_n-1 + L_n-2 with L₁ = 1 and L₂ = 3, complete the following table. What do you notice about the numbers in the last two columns?