Question

Generate the first 5 terms of this sequence:

f(1) = 0 and f(2) = 1, f(n) = f(n - 1) + f(n - 2), for n > 2.



0, -1, 1, 0, 2

0, 1, 1, 2, 3

0, 1, 2, 2, 3

0, 1, 1, 2, 2

Answer 1

i dont understand how to solve this.

Answer 2

f(1) = 0 and f(2) = 1 are given

keep this in mind

Answer 3

those are the first two terms

the third term is...

f(n) = f(n - 1) + f(n - 2)

f(3) = f(3 - 1) + f(3 - 2) ... replace EVERY n with 3 (third term is when n = 3)

f(3) = f(2) + f(1)

f(3) = 1 + f(1) ... replace f(2) with 1, because f(2) = 1 (given)

f(3) = 1 + 0 ... replace f(1) with 0, because f(1) = 0 (given)

f(3) = 1


So the third term is 1. The sequence so far is: 0, 1, 1

Answer 4

Using this idea, what is f(4) ?

Answer 5

it would be 2

Answer 6

good

Answer 7

so it would be B then

Answer 8

f(5) = ??

Answer 9

it would be 3

Answer 10

and correct, the final answer is B

Answer 11

yep f(5) = 3

Answer 12

short way to summarize this rule: to get any term, just add the previous two terms

Answer 13

thank you that helped I'm put it in my notes

Answer 14

you're welcome