Science Forums

# Sequences

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Hi,

I really need some help with a maths assignment. I am supposed to choose a sequence in which I can find a few rules/relations that apply to it. However, I am having trouble finding a sequence, as I am not allowed to use Fibonacci's sequence, pascal's triangle, square numbers and triangular numbers. Could anyone spare me a simple sequence that is pretty easy to understand?

Thanks!

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Arithmetic progression? How about geometric progression? Could mix them up to get an arithmetico-geometric progression.

Oooh- harmonic progression is cool too.

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Hi,

I really need some help with a maths assignment. I am supposed to choose a sequence in which I can find a few rules/relations that apply to it. However, I am having trouble finding a sequence, as I am not allowed to use Fibonacci's sequence, pascal's triangle, square numbers and triangular numbers. Could anyone spare me a simple sequence that is pretty easy to understand?

Thanks!

Pascals trinagle is made up of triangular numbers anyway so that's a push. Both square numbers and triangular numbers belong to the larger group of figurate numbers(sometimes called poygonal numbers), so if there is no restriction on that larger group you can choose 5-sided numbers (pentagonal), 6-sided (hexagonal) etcetera. Here's the generalized expression of figurate numbers>>> (n/2)*((s-2)*n)-s+4

s is the number of sides [if s=3 you get triangular numbers], and n is the ordinal in the list, the nth s sided number.

Hope this helps. :)

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As long as your assignment places not no restrictions on your sequence (such as never repeating), almost any made-up set of rule will generate a pretty interesting one. For example:

• If numeral contains no 2 digits the same, add 1 to it and square the result
• Otherwise, divide it by 10, discarding the remainder

produces: 1 4 25 676 67 4624 462 214369 45954496900 4595449690 459544969 45954496 4595449 459544 45954 4595 459 211600 21160 2116 211 21 484 48 2401 5769604 576960 57696 5769 33292900 3329290 332929 33292 3329 332 33 3 16 289 84100 8410 70744921 7074492 707449 70744 7074 707 70 5041 25421764 2542176 254217 25421 2542 254 65025 6502 42289009 4228900 422890 42289 4228 422 42 1849 3422500 342250 34225 3422 342 117649 11764 1176 117 11

Weaponry_angel, I suggest you just let your imagination run wild on this one – it appears to be a “no wrong answer” assignment.

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Oh! I'm sorry guys, but I forgot to mention that it has to be a well-known sequence... that's what I've been having trouble finding. I'll take a look at your suggestions though!

thanks for replying as well! :)

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Oh! I'm sorry guys, but I forgot to mention that it has to be a well-known sequence... that's what I've been having trouble finding. I'll take a look at your suggestions though!

thanks for replying as well! :)

;) Well known is such a relative phrase, however the figurate numbers were first described a couple thousand years ago. Leonard Euler loved them as well I hear.

:hihi: In simplest terms, when deriving figurate/polygonal numbers one is skip adding from the set of cardinal numbers. (Seldom if ever mentioned is the fact the cardinal numbers are the 2-sided numbers) Triangular numbers are the sum of each succesive cardinal number, square numbers are the sum of every second cardinal number, pentagonal numbers are the sums of every 3rd cardinal number & so on.

Fermat proved that any cardinal number is the sum of no more than 3 triangular numbers, or 4 square numbers, or 5 pentagonal numbers, etcetera. :)

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Oh! I'm sorry guys, but I forgot to mention that it has to be a well-known sequence... that's what I've been having trouble finding.
Does it have to be integer (whole number) valued.

There are many interesting, well-known real-values sequences. Ones that generate [math]\Pi[/math] are particularly popular.

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• 5 weeks later...

Check out Leibniz's formula for pi. While slowly-converging, it's still interesting. Leibniz formula for pi - Wikipedia, the free encyclopedia. There's always the harmonic series (which is interesting because the limit of the nth term approaches zero but the series diverges), hyperharmonic series, and in relation to these, the Riemann Zeta Function. Then there are the Euler numbers and the Bernoulli numbers, which are always fun. Euler number - Wikipedia, the free encyclopedia Bernoulli number - Wikipedia, the free encyclopedia

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