20th term in the fibonacci sequence

Anthony Hodsdon

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Sep 24, 1997, 3:00:00 AM9/24/97

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In article <19970925002...@ladder02.news.aol.com>,
ima...@aol.com (IMAJUMP) wrote:

> I am on an algebra scavenger hunt.I need to find out the 20th term of the
> fibonacci
> sequence.Can you help me?
>
>
>
> thank you :-)

F(n)=1/sqrt(5) * (((1+sqrt(5))/2)^n-((1-sqrt(5))/2)^n)

So, the number you require is 6765

Good Luck!

Anthony Hodsdon

IMAJUMP

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Sep 25, 1997, 3:00:00 AM9/25/97

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Bruce W Appleby

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Sep 25, 1997, 3:00:00 AM9/25/97

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ima...@aol.com (IMAJUMP) writes:

>I am on an algebra scavenger hunt.I need to find out the 20th term of the
>fibonacci
>sequence.Can you help me?

Incidentally Fibonacci was a person, Leonardo of Pisa, and probably
deserves to have his name capitalized.

You could use the recurrence F(n+1)=F(n)+F(n-1) together with F(1)=F(2)=1
and calculate it, but I rather like the formula:

F(n)=(((1+sqrt(5))/2)**n + ((1-sqrt(5))/2)**n) / sqrt(5)

So the answer is:

F(1)=1
F(2)=1
F(3)=1+1=2
F(4)=2+1=3
F(5)=3+2=5
F(6)=5+3=8
F(7)=8+5=13
F(8)=13+8=21
F(9)=21+13=34
F(10)=34+21=55
F(11)=55+34=89
F(12)=89+55=144
F(13)=144+89=233
F(14)=233+144=377
F(15)=377+233=610
F(16)=610+377=987
F(17)=987+610=1597
F(18)=1597+987=2584
F(19)=2584+1597=4181
F(20)=4181+2584=6765

Or, using the other method:

F(20)=6765

But you should check it; I could be (and frequently am) wrong.

Bruce
bapp...@world.std.com
Almost all calculations performed with the aid of electromechanical
devices, thereby adding to the number of ways I could have made a mistake.

Gary Scott Simon

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Sep 25, 1997, 3:00:00 AM9/25/97

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(e-mailed and posted)

In article <19970925002...@ladder02.news.aol.com>,
ima...@aol.com (IMAJUMP) wrote:

>I am on an algebra scavenger hunt.I need to find out the 20th term of the
>fibonacci
>sequence.Can you help me?
>
>
>

>thank you :-)

The Fibonacci sequence begins with with two ones and each subsequent
term is the sum of the two immediately preceeding it.

The ratio of each term in the sequence to the one immediately
preceding it approaches the so-called "golden proportion", representing
the most visually pleasing ratio of width to height in artwork. This
ratio is often found in nature.

Edward Huyer

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Sep 25, 1997, 3:00:00 AM9/25/97

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ima...@aol.com (IMAJUMP) wrote:

-->I am on an algebra scavenger hunt.I need to find out the 20th term of the
-->fibonacci
-->sequence.Can you help me?

The fibonacci sequence up to and including the twentieth number is:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
2584, 4181, 6765
Edward Huyer
Arcanum
Clan Ash
arc...@stealthmail.com
ICQ# 1667646

Yvan Haine

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Sep 26, 1997, 3:00:00 AM9/26/97

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The first term of Fibonnacci sequence is 1, the second is 2 and all the
next are the sum of the two preceding.
So 3rd is 3 (=1+2),
4th is 5 (=2+3)
5th is 8 (=3+5),...
you just have to go on

Yvan

IMAJUMP <ima...@aol.com> a écrit dans l'article
<19970925002...@ladder02.news.aol.com>...

> I am on an algebra scavenger hunt.I need to find out the 20th term of the

nob...@nowhere.on.ca

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Sep 26, 1997, 3:00:00 AM9/26/97

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On 25 Sep 1997 00:29:24 GMT, ima...@aol.com (IMAJUMP) wrote:

>I am on an algebra scavenger hunt.I need to find out the 20th term of the
>fibonacci
>sequence.Can you help me?

>thank you :-)

Try this:

REM FIBONACCI SEQUENCE
REM EACH ELEMENT IS THE SUM OF THE PREVIOUS TWO
REM ASSUME THE FIRST TWO ELEMENTS ARE EACH 1
CLS
PRINT "FIBONACCI SEQUENCE"
INPUT "NUMBER OF ELEMENTS "; Y
DIM F(Y)
F(1) = 1: F(2) = F(1)
FOR K = 3 TO Y
F(K) = F(K - 1) + F(K - 2)
NEXT K
FOR K = 1 TO Y
PRINT F(K); " ";
NEXT K
END

Craig Lambert

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Oct 1, 1997, 3:00:00 AM10/1/97

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IMAJUMP <ima...@aol.com> wrote in article
<19970925002...@ladder02.news.aol.com>...

> I am on an algebra scavenger hunt.I need to find out the 20th term of the
> fibonacci
> sequence.Can you help me?
>
>
>
> thank you :-)
>

The first two terms of the fibonacci sequence are 1. and each term
thereafter is calculated by summing the previous 2 terms. But there is a
direct way to calculate the nth term without having to find all the
previous terms.

The general formula for the nth term of the fibonacci sequence is:

f(n) = (a^n - b^n) / sqrt(5)

where a = (1+sqrt(5))/2 and b = (1-sqrt(5))/2

Not that this is any easier, but if you wanted to calculate the 10,000 th
term, it may come in handy.