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

The next number is 3. So you plug in n = 3.

Answer 2

f(3) = f(3 - 1) + f(3-2)
Solve.

Answer 3

That would be: f(3) = f(2) + f(1)

Answer 4

Now plug in for f(2) and f(1).
f(3) = 1 + 0

Answer 5

f(3) = 1

Answer 6

Do the same for 4 and 5. Tell me if you need help.

Answer 7

Im not really good with these problems. Can you explain to me how to do it correctly?

Answer 8

Yeah

Answer 9

Now we can plug in 4.

Answer 10

Tell me if you need help.

Answer 11

I dont mean like whats the next thing i do in this problem. I wanna know how to do any problems that are similar to this one

Answer 12

Plug in 4.
so, here is our original equation.
f(n) = f(n - 1) + f(n - 2)
n is just a variable.
so for n, we plug in 4.
f(4) = f(4-1) + f(4 - 2)

Answer 13

Can you solve for f(4) = f(4-1) + f(4 - 2)

Answer 14

f(4) = f(4) -1 + f(4) -2?
Or f(3) + f(2)
One of these ways?

Answer 15

The second is correct!

Answer 16

Now we plug in!
Since we already know:
f(3) = 1
f(2) = 1

f(4) = 1 + 1

Answer 17

That means f(4) = 2

Answer 18

Lets clean this up!

f(1) = 0
f(2) = 1
f(3) = 1
f(4) = 2
f(5) = ?

Answer 19

We need to find one more!

Answer 20

f(4) + f(3) ?

Answer 21

Yes!

Answer 22

Now, plug in the numbers.

Answer 23

This last part is what gets me kind of confused.
I got the f(4) + f(3)
Do i go like this?
f(4) = 1
f(3) =1
f(5) = 2?

Answer 24

f(4) = 2 actually.
We know this because when we solved for f(4) already.
These problems are in a series of steps, to get one answer you have to know other so on and so on.

Answer 25

See, when we solve for
f(4) = f(4 - 1) + f(4 - 2)
f(4) = f(3) + f(2)
f(4) = 1 + 1
f(4) = 2

Do you see how we had to know what f(3) and f(2) were to know what f(4) is?

Answer 26

Since we are solving for f(5) we had to know what f(4) is, and we do, because we did the equation before hand.

Answer 27

so its f(5) = 3?

Answer 28

Great job!

Answer 29

Do you want to see what f(6) is for extra help?

Answer 30

Sure. f(6) = f(6-1) + f(6 - 2)
f(6) = f(5) + f(4)
F(6) = 4?

Answer 31

Remember that f(5) = 3 and f(4) = 2

Answer 32

so, f(6) = 3 + 2
f(6) = 5

Answer 33

So for f(7)
f(7) = f(7-1) + f(7 - 2)
f(7) = f(6) + f(5)
f(7) = 5+3?
Do i take the last two answers?

Answer 34

Yes! Very good!

Answer 35

This is known as a recursive formula.

Answer 36

It needs previous answers to make the new answer.

Answer 37

f(8) = f(8-1) + f(8 - 2)
f(8) = f(7) + f(6)
f(8) = 8 + 5?

Answer 38

Great! You are getting the hang of it. Now, since it just needed the first 5, we already have the answer. Do you which one it is?

Answer 39

The second option

Answer 40

Great!

Answer 41

Thanks!

Answer 42

No problem! Do you want extra practice?

Answer 43

Sure

Answer 44

f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2.
Solve for the first 5

Answer 45

I am going to have to go soon, but if you need any help you can message me, :)

Answer 46

Ok thanks. Ill practice these in my notebook.

Answer 47

No problem. Thanks for the metal!