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.
A. 0, -1, 1, 0, 2
B. 0, 1, 1, 2, 3
C. 0, 1, 2, 2, 3
D. 0, 1, 1, 2, 2
Please helppp! Thanks! <3

- anonymous

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- schrodinger

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- myininaya

f(n)=f(n-1)+f(n-2)
Try replacing n with 3
like so
f(3)=f(3-1)+f(3-2)
f(3)=f(2)+f(1)
You know what f(2) equals and you know what f(1) equals
f(2)=1 and f(1)=0
Replace f(2) and f(1) with 1 and 0 respectively
and then add those values to get f(3)

- anonymous

Um...
f(3) = f(1) + f(0)
So, f(3) equals 1?
How do I get all those other numbers in the choices? :o

- myininaya

you keep going up with n

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## More answers

- myininaya

find f(4) using the same f(n)=f(n-1)+f(n-2) formula

- myininaya

then do f(5) and so on...

- anonymous

... But what //is// f(5)? Idk I've been doing this for like an hour and the lesson is horrible at describing it. :(((

- anonymous

And I'm not supposed to find f(5), I think... I'm supposed to find 5 terms or something.

- myininaya

f(1), f(2),f(3),f(4),f(5) are the numbers in your sequence.
f(1) and f(2) are given
we just found f(3) given f(n)=f(n-1)+f(n-2)
then we do the same for f(4) and f(5)
Evaluate:
f(4)=f(4-1)+f(4-2) and f(5)=f(5-1)+f(5-2)

- myininaya

You must do f(4) before you do f(5) though

- myininaya

Since to evaluate f(5), you will need to know f(4) and f(3)

- anonymous

f(4) = f(4-1) + f(4-2)
f(4) = f(3) + f(2)
f(4) = 5?
_________
f(5) = f(5-1) + f(5-2)
f(5) = f(4) + f(3)
f(5) = 7?
Is this correct?

- myininaya

No...

- anonymous

...? I don't understand. D:

- myininaya

So f(1)=0
f(2)=1
f(3)=f(3-1)+f(3-2)
=f(2) +f(1)
But we are given that f(2) is 1 and f(1) is 0
So we replace f(2) with 1 and we replace f(1) with 0
like so
=1 +0
=1
So we just concluded as we concluded earlier that f(3) is 1 not 3

- myininaya

Now to find f(4)
You use the same formula
f(n)=f(n-1)+f(n-2)
this is the same formula we used to evaluate f(3)
We will use this formula over and over until we are done finding numbers in the sequence (which this sequence goes on forever)
So anyways f(4)
Replace n with 4
f(4)=f(4-1)+f(4-2)
=f(3) +f(2)
Recall we just found f(3) and f(2) was given to us.

- anonymous

... I am so confused. Okay so the formula comes out to ... f(4) = f(1) + f(1)? ??? ??
So the answer is 2?
Does that make the answer to the entire problem C? :S

- myininaya

well f(3) is just one not f(1)
and
f(2) is just one not f(1)

- myininaya

f(1) is not equal to f(2)

- myininaya

but 1 is equal to f(2)

- myininaya

but yes 1+1 is equal to 2

- anonymous

But in the problem... it says " f(2) = 1"?

- myininaya

yes f(2) =1 but f(2) does not equal f(1)
f(1) is 0
0 is never 1
so
f(2) is never f(1)
because they hold different values

- anonymous

Oh. I thought they were the same lol w/e.
So is the answer C or do I have to waste my time farther into the problem?? :o

- myininaya

I'm pretty sure that is not what we got...

- myininaya

the first five terms are f(1),f(2),f(3),f(4),f(5)
we have that f(1)=0, f(2)=1, f(3)=1, f(4)=2,....

- anonymous

Ohhh or it could be B or D. I know it isn't A...

- anonymous

Ugh so I have to do more. x_x Math sucks omfg. Okay so lemme figure out the 5 term thingy.

- myininaya

You don't have to do more.

- anonymous

Oh?

- myininaya

You just aren't realizing what we got for the first 4 numbers I guess

- anonymous

Well two choices have "0, 1, 1, 2" as the first four numbers...

- myininaya

Yep that is right

- myininaya

0,1,1,2,....

- myininaya

So yeah we do have go one more because b and d both begin with that
(sorry didn't realize)

- myininaya

I leave finding f(5) to you

- anonymous

Whats the equation thingy??

- myininaya

f(n)=f(n-1)+f(n-2)
this is the same one we have been using

- myininaya

If we want to find f(5) and we are given f(n)=f(n-1)+f(n-2)
then in order for f(n) and f(5) to be the same n would have to be 5.
So replace all the n's you see in f(n)=f(n-1)+f(n-2) with 5.

- anonymous

f(5)=f(5-1)+f(5-2)
f(5) = 4 + 3
f(5) = 2 + 1
f(5) = 3
So it's "B," right?

- myininaya

You mean that f(5-1) is equal f(4) and that f(5-2) is equal to f(3)
You only performed the inside operation
You haven't even used f
So You should have
f(5)=f(5-1)+f(5-2)
=f(4) + f(3) because 5-1 is 4 and 5-2 is 3
=2 + 1 because f(4) is 2 and f(3) is 1
=3
The answer is right
Just the work was a little off.
But yes now we can say what the answer is

- anonymous

Yeah I don't need to show my work. Math is stupid so as long as I have the right answer, I'll pass. :) Hey, can you help me check the answer I found on the first part of a different question? Just so I know I'm on the right path to the correct answer?

- myininaya

Math isn't stupid.

- myininaya

Math is in everything.

- anonymous

Lol I'm more of a calculator type of girl, myself. I'm a writer so it's not as important to me (unless someday a girl behind the cash register at the grocery store makes me solve a complicated equation about substitutions for x or whatever (with work shown!) LOL) So yeah, anyways, can you help just check my answer for the first part of this thing? I need to get this work done so I don't fail World History. D:

- anonymous

(I'm homeschooled so my douchy World History teacher is going to call me in like 15 minutes and ask a bunch of questions I'll end up blundering on x_x. Next semester I'm going back to brick and mortar before I flunk World History and Algebra completely. lol)

- myininaya

Well, I would have to say it would help you and I have if you had a more positive attitude about math.

- myininaya

And any of your future math tutors.

- anonymous

Yeah any positivity on the subject more along the lines of me looking forward to the bright horizon: the time that I'm allowed to stop taking math classes. Lol.
I guess what motivates me is the "It'll be over soon~" idea like soldiers on the battlefield or somebody starving to death in the wilderness. I'd like to get it done and not have math bring down my 4.0 GPA. x_x I've always sucked at it, no matter how hard I try, and I don't like the subject in general (In my opinion, it's a bit impractical. Nobody I've ever met that isn't in a field like architecture or something has ever meticulously plotted graph points. And the only fractions I've ever found to be actually necessary in real life are 1/2, 1/3, and 1/4, basically.)
I guess I'll never be a mathematician. *shrugs* Oh well. Lol.

- myininaya

Go ahead and post your other problem.

- anonymous

Okay. :)
"Find f(5) for this sequence:
f(1) = 2 and f(2) = 5
f(n) = f(1) + f(2) + f(n - 1)
n > 2.
f(5) = ______ "
This is the problem. I made this equation:
f(3) = f(1) + f(2) + f(3 - 1)
So, with this, I ended up making:
f(3) = 2 + 5 + f(3 - 1)
The "f(3 - 1)" part is confusing me. I don't know what to do with this section as I try to evaluate the terms. D:

- myininaya

3-1 equals 2

- myininaya

so what is f(3-1) equal to?
f(3-1) is equal to f(2)
and f(2) is given to you in the problem

- anonymous

Oooh! Okay, I didn't think about it that way.
f(3) = 2 + 5 + 5
f(3) = 12
Is this correct? (My original answer wasn't at all; I got 9 somehow. Lol)

- myininaya

that is right! good job!

- anonymous

Okay! :))
Now one last question; how do I translate that into finding the 4th term?
f(4) = f(1) + f(2) + f(4 - 1)
f(4) = 2 + 5 + 12
Does it look like this to solve it? :3

- myininaya

Yep! That is great. I think you are getting it.

- anonymous

Okay! Thanks for all your help! :D

- myininaya

I'm really happy that you are happy that you did it. :)
Now I must go.
Good luck on everything.

- myininaya

I gave you a medal for understanding by the way. :)

- anonymous

Great, thanks! :))

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