Question

Can someone help me to solve this sequence?
40 4 3 15 2 6 5 8 10 9 14 15 16 17 ...

Thanks

Answer 1

Solve, like find an explicit formula, an iterative formula, or just the next one or two terms?

Answer 2

Just the next term and an explanation

Answer 3

Not much of a pattern there. Not arithmetic, not geometric, would take a lot of work to fit a polynomial to it . . .

Answer 4

There are only 3 differnet types of sequences it can be. Geometric, Arithmetic, or Recursive. You have to find out which one it is and then move on from there. In an Arithmetic sequence there is a common difference in each succeeding number , so n2-n1=n3-n2. In a geometric is a ratio, (n2/n1)=(n3/2). For a recursive you just have to solve with your mind.

Answer 5

My bet is that its an recursive with an interesting equation as CLiff says.

Answer 6

We've been stairing at it for the past hour but have no clue

Answer 7

who has?

Answer 8

just here at home, it's a question in the preround of a quiz

Answer 9

There are infinite amount of solutions it could be. It could be that \[\Large F_{x+14} = \sum_{k=1}^{14}F_{x+k}\] and that this is just the initial sequence.

Answer 10

Indeed, finding patterns is a matter of induction, which is essentially making a conjecture (guess) and then justifying it using some features of the sequence.
I would say there is no pattern and just choose something arbitrary for the next term.

I tried graphing it, and it looks pretty chaotic, especially in the beginning, but seems to have a converging quality to it.

Answer 11

As Cliff says, you're screwed until you see the pattern and then find the mathematical explanation behind the pattern. I just suggest beefing up on your recursive skills and hopefully develop an intuition for recursive problems.

Answer 12

Honestly, it is probably just some dude's mutual fund right before some crash, and they just want to confuse you with it.

Answer 13

There really should be a solution, We've found answers to most other questions

Answer 14

You can still have a series with no pattern. WE have already ruled our geometric and arithmetic sequences. So the only options are that it is an elusive recursive that we cannot find or a sequence with no pattern. Its just that I cannot find a pattern and with recursive sequences its all about induction like Cliff said. There might be a solution its just that we can't find it.

Answer 15

k thanks anyhow

Answer 16

Sometimes there just isn't a pattern. Like I said, you could try fitting a thirteenth-degree polynomial to it, and that should give the most likely next point, but that is a pretty back-breaking process if you don't have some powerful linear algebra techniques.