Patterns

[dscsoccer20]

whats the pattern?

1, 3, 4, 7, 11, 18

 

[Deleted member 4993]

whats the pattern?

1, 3, 4, 7, 11, 18

4 = 3 + 1

7 = 3 + 4

11 = 4 + 7

a[sub:ekl1r8np]n[/sub:ekl1r8np] = a[sub:ekl1r8np]n-1[/sub:ekl1r8np] + a[sub:ekl1r8np]n-2[/sub:ekl1r8np]

This is also known as Fibbonaci's sequence - google it to learn more....

 

[soroban]

Hello, dscsoccer20!

What's the pattern? . \(\displaystyle 1,\:3,\:4,\:7,\:11,\:18,\:\hdots\)

This is the Lucas Sequence.


It begins with 1 and 3.

Thereafter, each term is the sum of the preceding two term.


The Fibonacci Sequence begins with 1 and 2: .1, 2, 3, 5, 8, 13, . . . **

Lucas started the sequence with 1 and 3 . . . and had the sequence named for him.


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


It can be argued that the Fibonacci Sequence begins with 0 and 1:

. . 0, 1, 1, 2, 3, 5, 8, 13, 21, . . .

 

[Denis]

Lucas started the sequence with 1 and 3 . . . and had the sequence named for him.

Ha ha: I'm hereby immortalizing myself with the "Denis sequence": 1,4,5,9,14.....
You wanna the 1,5,6... Subhotosh? You can be my assistant :roll:

 

[Deleted member 4993]

Lucas started the sequence with 1 and 3 . . . and had the sequence named for him.

Ha ha: I'm hereby immortalizing myself with the "Denis sequence": 1,4,5,9,14.....
You wanna the 1,5,6... Subhotosh? You can be my assistant :roll:

Hey ... hey .. who let you out of the corner.....

Actually I wanted the 1000, 1000, 2000, 3000, 5000, ...... series.

But in defense of Lucas and Soroban, Lucas series does have some unique properties - different from Brother Fibbonacci's sequence (however i forget those and I am too tired to google it ... so I'll go to the corner before Denis gets me.....)

 

[soroban]

For some reason, I still remember these:


. . \(\displaystyle F(n) \;=\;\frac{(1+\sqrt{5})^n - (1 - \sqrt{5})^n}{2^n\sqrt{5}}\)

. . \(\displaystyle L(n) \;=\;\frac{(1+\sqrt{5})^n + (1 - \sqrt{5})^n}{2^n}\)