Recursive Sequence

Question

(1,2,3,4,8,32)

N_i = N_i-1 N_i-2

This is a sequence and a recursive definition. Can someone explain how to input these numbers into this definition?

Answer 1

1, 1,2, 2, 4, 8, 32, 256, ...

N1 = 2

N2 = 1

N3 = 2 = N2(N1) = 1(2) =2

N4 = 2 = N3(N2) = 2(1) = 2

N5 4 - N4(N3) = 2(2) = 4

N6 =8 = N5(N4) = 4(2) = 8

N7 = 32 =N6(N5) = 8(4) =32

N8 = 256 = N7)N6) = 32(8) = 256

this might be the more accurate sequence, with the "3" a typo which should have been a "2"

each term is the product of the previous two terms, similar to a Fibonacci sequence where each

term is the sum of the previous two terms.

Answer 2

For the sequence 1,2,3,4,8,32 and the notation

N_i = N_i-1N_i-1

The i-1 means one term before and i-2 means the term before the last term.

So you have to start with the 3rd term

N₃ = N₂N₁

If the sequence is 1,2,2,4,8,32 instead, then the recursive definition works. Must be a typo.

N₁ = 1

N₂ = 2

N₃ = 2×1 = 2

N₄ = 2×2 = 4

N₅ = 4×2 = 8

N₆ = 8×4 = 32