Please give the next 3 terms of this sequence with the formula, or explanation if possible:
1, 2, 3, 8, 15, 48, 105, 384, 945......
Thanks for any help.

Guest Apr 15, 2017

I think i got the answer.



The sequence can be described by the following formula: an+2=an*(n+2), a1=1 and a2=2


That means the next 3 terms are: 384*10=3840, 945*11=10395, 3840*12=46080


But there is something else i want to add about this type of questions:


I feel its a little bit silly, because you could always find another pattern or another way. Of course, if you need to answer that type of questions in a test, you cant write that, you'll have to do what they expect you to do. But i feel its wrong NOT to mention what im going to.


I once heard a joke about a mathematician that has an interesting way of answering those questions: he simply writes "19" when he's asked to find the next term. He justifies that with one of the theorems of a famous mathematician called Lagrange. And in my opinion he's right. Saying that there is a finite amount of answers is silly, because there isnt. There is always a way to make order out of what seems to be chaos.


I dont know if you love math or care about it, but if you do, remember it.

Ehrlich  Apr 15, 2017

True, what you say! The more patterns you see and can explain clearly and coherently the better!.

However, in this sequence, I see a VERY CLEAR pattern, which is very familiar to me!


The sequence is: 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10,395, 46,080......etc.
This is the double factorial function of all positive integer 1, 2, 3 4,.....etc. It is a generalization of the usual factorial n! defined by n!!. For odd n {n·(n - 2)...5·3·1, the product is odd.  For even n·(n - 2)...6·4·2, the product is even.  Note that -1!! = 0!! = 1, by definition. 

Guest Apr 15, 2017

Very nice, Erlich  and Guest.........!!!



cool cool cool

CPhill  Apr 15, 2017

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