Recursive Rule Questions

Question

Write a recursive rule for the sequence.

a, b, a+b, a+2b, 2a+3b, 3a+5b,

Answer 1

Let's look at how the coefficients evolve to determine the recursive rule...

These are seed values for the recursive rule...

a --> 1, 0

b --> 0, 1

a+b --> 1, 1

a+2b --> 1, 2

2a+3b --> 2, 3

3a+5b --> 3, 5

We see the sequence for 'a' appears to follow the fibonacci sequence a_n = a_n-1 + a_n-2 as does the 'b' sequence but it is shifted ahead by one...

The fibonacci sequence has 0,1,1,2,3,5,8,13,21,...

Let the fibonacci numbers be defined as F_n = F_n-1 + F_n-2 (This is the standard form for recursive calculating the n^th number).

F_n-1 * a + F_n * b for any value of n ≥ 1