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

#1**+1 **

I think i got the answer.

The sequence can be described by the following formula: a_{n+2}=a_{n}*(n+2), a_{1}=1 and a_{2}=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

#2**+1 **

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