Fibonacci numbers are generated using a recursion rule that relates each number to the t...

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 T_n = T_n-1 + T_n-2 + T_n-3 + T_n-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?