a_n =2a_n-1 - a_n-2 ; where a0=1 and a1=3 ...WTF?

Question

and then it gets put backwards and goes like b_n =b_n-1+2b_n-2 ; where b0=1 and b1=2? How do you solve these?

Answer 1

let's look at the a series. it starts out 1, 3, .... The next term, by the definition, is 2(3) - 1 = 5. so we have 1, 3, 5, .... The next term is 2(5) - 3 = 7. These are clearly the odd numbers, where a_n = 2n - 1.

with b series, it starts 1, 2, ..., and the next term is 2 + 2(1) = 4, so 1, 2, 4, .... The next term is 4 + 2(2) = 8, and we have powers of 2, so b_n = 2^(n-1).

Answer 2

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