Question

Do anyone know how Fibonacci Sequence works?? and what if they give you a question on like sum of the first 14 terms in the Fibonacci Sequence, how do i find it? help!!!

Answer 1

The first numbers in the sequence are 0 and 1, and every number thereafter is the sum of the previous two numbers.

Answer 2

i still don't get it is it like adding?

Answer 3

The function is \(f_{n} = f_{n-1} + f_{n-2}\).

That means that any given number in the series is the sum of the number before it and the number before that number.

Like I said, the first two numbers in the sequence are 0 and 1. Therefore, the third number would be 0+1, which is 1. The fourth number would be 1+1, which is 2. The fifth number would be 2+1, or 3. The sixth number would be 3+2, or 5. And so on.

Answer 4

what is the n-1 and n-2

Answer 5

So, if you were to write out the series so far, you would have 0,1,1,2,3,5 ...

Answer 6

\(n\) is the term. So, if you're looking for the fifth term in the series, \(n\) = 5. Therefore, the fifth term (\(f_{5}\)) is equal to \(f_{5-1} + f_{5-2}\), which is \(f_{4} + f_{3}\) (the sum of the fourth and third terms in the series).

Answer 7

ok thanks

Answer 8

So let's actually try it. If we wanted \(f_{5}\), we know we need to add \(f_{4} \text{ and } f_{3}\). Since those are 2 and 1, we know that \(f_{5} = 3\).

Answer 9

hummmmmmm..... so since you were looking for 5 you added 2 and 1 and thats why you got f5=3

Answer 10

I was looking for the fifth term in the series, yes. It requires, of course, that I know n-1 and n-2 (in this case, the fourth and third terms, respectively). If you wanted the tenth term but didn't know the eighth and ninth, the formula I gave would be useless. You can of course figure them out one-by-one until you get where you need.

Answer 11

I think you can figure out any number in the series using the square root of 5, but that's more advanced mathematics.

Answer 12

so i would use the formula until i can find the ten if i wanted to right like if it started from 1

Answer 13

Sure, that's one way, although certainly not very efficient if you needed the sum of the first 100 terms.

Answer 14

oh i see...

Answer 15

This appears to be Binet's formula; I'm not sure if it applies.

\[f_{n} = \frac{(\frac{1+\sqrt{5}}{2})^{n}-(\frac{1-\sqrt{5}}{2})^{n}}{\sqrt{5}}\]

Answer 16

i think thats another way to find the answers but i know thats part of fibonacci sequence

Answer 17

but im not sure what it is used for

Answer 18

i look it up http://www.mathsisfun.com/numbers/fibonacci-sequence.html

Answer 19

its at the bottom but it only explains it gets a whole number

Answer 20

is it a system of working backward

Answer 21

Okay, I must have made a mistake then, because I started with a formula similar to that.

So:

\[f_{n} = \frac{(1.618034)^{n} - (-0.618034)^{n}}{\sqrt{5}}\]
I tried \(f_{8}\) and got 21, which is right.

Answer 22

did you divide to get 1.618034 and -0.618034

Answer 23

No, calculate each of them to the power of n, then find the difference, and then divide that by the square root of 5.

Answer 24

ohh i see

Answer 25

Don't worry about how to get 1.628... and -0.618... well, if you want to know, you can look on Wikipedia.

Answer 26

ok thank you

Answer 27

They're just \(\frac{1+\sqrt{5}}{2}\) (which is 1.618...) and \(\frac{1-\sqrt{5}}{2}\) (which is -0.618...).

Answer 28

i didnt know there was so many rules on Fibonacci Sequence

Answer 29

Yeah, it's a pretty powerful concept.