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

This is a rather well known sequence :D
\[\Large \left.\begin{matrix}f(1)&f(2)&f(3)&f(4)&f(5)\\0&1&?&?&?\end{matrix}\right.\]

Answer 2

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

So what happens when n = 3?

Answer 3

n=2

Answer 4

it would be 2 3 4 after that ?

Answer 5

yes

Answer 6

would the answer be C

Answer 7

I don't know, what's f(3)?
Use the fact that f(n) = f(n-1) + f(n-2)

Answer 8

n-1 would be 2 and n-2 would be 1?

Answer 9

That's good :)
so f(3) = f(2) + f(1)
Which is...?

Answer 10

6?

Answer 11

Don't be silly :P
You're already given the values of f(2) and f(1)

Answer 12

\[\Large \left.\begin{matrix}\color{blue}{f(1)}&\color{blue}{f(2)}&f(3)&f(4)&f(5)\\\color{red}0&\color{red}1&?&?&?\end{matrix}\right.\]

Answer 13

0 1 2 2 3?

Answer 14

I don't know, let's find out together, but step-by-step.

Now, what's f(3) = ?

Answer 15

2

Answer 16

How did you get 2?

Answer 17

just going 1 number less than 3

Answer 18

since it looks like the others did that

Answer 19

I told you to follow this formula (as it is said in your problem)
f(n) = f(n-1) + f(n-2)

Set n = 3, and find f(3)

Answer 20

i got 3

Answer 21

How?

Answer 22

plugging in 3 where n is

Answer 23

Okay... so how did you get 3?

Answer 24

I don't see how you could get 3 by plugging in n = 3...

Answer 25

(3-1)=2 + (3-2)=1 and i just added it to 3 i dont get it

Answer 26

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

Please plug in n = 3 again, but be very careful when evaluating.

Answer 27

what did i do wrong

Answer 28

It's not (3-1) and (3-2) which you add, it's f(3-1) and f(3-2)
which are totally different.

Answer 29

so what do i do with the f

Answer 30

you multiply?

Answer 31

It's a function.
And as I have said before, you ARE given the values of f(1) and f(2)

Answer 32

i think its C

Answer 33

But why?

Answer 34

because it looks like thats how the pattern goes am i wrong

Answer 35

follow pony

Answer 36

I strongly advise against guessing ^_^

Answer 37

is my guess wrong

Answer 38

Let's find out.
Starting with you figuring out f(3)
from the formula
f(n) = f(n-1) + f(n-2)

Answer 39

f(2)=1

Answer 40

f(1)=0

Answer 41

f(3)=2

Answer 42

so 1+0=1

Answer 43

what do you think

Answer 44

what do i think is the answer?

Answer 45

Just f(3) for now. How do you get 2?

Answer 46

3-1=2

Answer 47

But why would you do 3-1?

Answer 48

n-1 u plug in the 3

Answer 49

but n-1 isn't the expression to plug n = 3 in

It's
f(n) = f(n-1) + f(n-2)