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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi guys

find the one equality general term formula for the sequence:

3,6,8,16,18,36,38,76,78,...

The general term formula must not be defined partially,but must contain only one equality.

*Last edited by anonimnystefy (2012-03-31 00:29:15)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I really wonder if anyone will get that one.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,382

OK OK, only just got in. I'm working on it.

Would the next two terms be

156, 158 ?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Yes,those are the next two terms.

The term are gained by repeatedly multiplying by 2 and the adding 2.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi gAr

Nice work.Congrats also for showing me that there is another formula.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Thanks for the problem.

What's your formula?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi gAr

You're welcome.

Iwill post my formula in a few mintes,so stay put.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay...

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

*Last edited by anonimnystefy (2012-03-31 02:12:21)*

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I'm getting a(1) = 12 for your formula?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

{1/2}=1/2

{1}=0

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Oh, okay.

Now I'm getting a(2) = 2*(5√2 - 2)*(1)

Did I substitute for n correctly?

*Last edited by gAr (2012-03-31 02:35:20)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

if I remember correctly (1-1)/2=0

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

wait a sec! i typed it out wrong.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

*Last edited by anonimnystefy (2012-03-31 02:50:56)*

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I thought that was (2-1)/2 = 1/2

and hence 2*(5*2^(1/2)-2)*1 ?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

look at #16.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Looking at it...

Meanwhile, there's some problem with the LaTeX code, can you correct it?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

I fixed the LaTeX code.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

The formula's correct now.

Thanks.

LaTeX code's also fine, thanks.

*Last edited by gAr (2012-03-31 02:53:07)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

Thank you as well for your formula.Your seems better because it doesn't use the {a} "function".

Who knows,maybe bob finds a third one.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

You're welcome.

I just combined two recurrences for odd and even terms, and the CAS derived the closed form for me.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

cool.I wonder if anything can be done using G.F.'s?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,382

hi Stefy and gAr

Haven't been looking at yours so who knows.

Here is mine:

Please don't ask me to simplify it. Sob and tears.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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