Question

Generate the first 5 terms of this sequence:

f(1) = 1 and f(2) = 2, f(n) = f(n - 1) + f(n - 2), for n > 2.

(a) 1, 2, 3, 4, 5
(b) 1, 2, 3, 5, 7
(c) 1, 2, 3, 5, 8
(d) 1, 3, 5, 7, 9

If you could just help understand how to set up the problem and solve it, that would be great. :)

Answer 1

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Answer 2

find: f(1), f(2), f(3), f(4), f(5)

they give you the first 2, and a formula to develop the others

Answer 3

f(n) = f(n - 1) + f(n - 2), for n > 2, so n starts at 3

f(3) = f(3 - 1) + f(3 - 2)
= f(2) + f(1) , and those values we are given

f(4) = f(4 - 1) + f(4 - 2)
= f(3) + f(2), we know f(2) from the start, and already found f(3)

f(5) amounts to f(4) + f(3) which would both have already been determined

Answer 4

@amistre64 So where I see the "n" I plug in the next number in the sequence? For 3, f(n) = f(n - 1) + f(n - 2) becomes f(3) = f(3 - 1) + f(3 - 2)? Am I on the right track?

Answer 5

that is correct

Answer 6

Okay thanks! I think I've got it from here.

Answer 7

;) good luck