Fibonacci numbers are generated using a recursion rule that relates each number to the two numbers that precede it. Similar sequences can be generated by using more than two numbers to determine a number in the sequence.
The Tetranacci numbers can be generated using the recursion rule Tn = Tn-1 + Tn-2 + Tn-3 + Tn-4, where T1 = 1, T2 = 1, T3 = 2, and T4 = 3.
a. Find the first 12 Tetranacci numbers.
b. Find the ratios of consecutive pairs of Tetranacci numbers from part (a); that is, calculate
What do you notice about the ratios?
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