Sequence question

1. Nov 17, 2003

MathematicalPhysicist

the next sries:6,10,14...62
62 is the tenth number in the series.
what is the fourth number?

my answer is 22 because the series is a multplication of 2 with a prime number starting from 3.
2*3,2*5,2*7,2*11...2*31

2. Nov 17, 2003

pnaj

Your rule works ... so it must be correct!!

Have confidence.

3. Nov 17, 2003

HallsofIvy

There exist an infinite number of sequences having the given values. Your rule works- that's all one can ask.

4. Nov 18, 2003

MathematicalPhysicist

"There exist an infinite number of sequences having the given values."
can you show me the other sequences?

5. Nov 18, 2003

Guybrush Threepwood

how about the sequence made from the first ten numbers repeated periodically?

6. Nov 18, 2003

MathematicalPhysicist

care to explain?

7. Nov 18, 2003

Guybrush Threepwood

2*3,2*5,2*7,2*11, ..., 2*31, 2*3,2*5,2*7,2*11, ..., 2*31, 2*3,2*5,2*7,2*11, ..., 2*31, 2*3,2*5,2*7,2*11, ..., 2*31, .......
and so on

8. Nov 18, 2003

MathematicalPhysicist

but it doesnt solve for the fourth number in this sequence or the 14 24 etc.

9. Nov 18, 2003

Guybrush Threepwood

why not?
the series begins as you said 6,10,14...62
the tenth number is 62, the fourth is 22...
you didn't specified anything about the 14th or 24th number.....
this is one of the infinite number of sequences HallsofIvy said (IMO)

10. Nov 18, 2003

pnaj

I think 'loop quantum gravity' just wants to know WHY there are infinitely many 'rules' that would produce a single sequence.

So, for a clear example, look at the sequence ...

2, 4, 6, 8, ...

Here are some 'rules' to describe it:

(a) {2n: n is a natural number}
(b) {2n/1: n is a natural number}
(c) {4n/2: n is a natural number}
etc.

Although there are infinitely many, all of them are just 'versions' of (a) and are NOT interesting or of any value.

Sometimes this is not the case, though, and two quite different 'rules' can produce the same sequence and both are 'interesting'.

11. Nov 18, 2003

HallsofIvy

But there doesn't have to be a simple rule-

I can just declare the sequence to be 6,10,14, -300, pi, &sqrt;(2)
10000, 999, -1,62, 1, 2, 3, 4, 5,.... with the rest being the positive integers in order.

I had a professor who gave us the sequence 21, 19, 17, 15, 13, and challenged us to find the next number.

The next number in the sequence was 32! Those were the numbers of the bus stops on his way to work. (Between 13 and 32, the bus turned off the main street it had been on.

12. Nov 18, 2003

jeffceth

good point. I think Occam's Razor is the most relevant principle to this question. Granted, there are an infinite number of possible solutions, but chances are the most basic, logical answer is the most useful(though not of necessity the only right answer).

jeffceth

13. Nov 19, 2003

MathematicalPhysicist

but the rule is the same as i pointed out, multiplication of a prime number by two.
i thought that in a sequence there could be infinite patterns to it.

14. Nov 20, 2003

Guybrush Threepwood

no it's not because after your rule, the 11th number is 2*37 = 74 and after mine it's 6. they're 2 different series....

I don't quite understand this.
If you define a sequence as being 2*(succesive prime numbers) there's only one sequence.
But if you define a sequence as 6, 10, 14, ..., 62, .... there a a infinite number of sequences that match. If there's nothing more in the definition any sequence you find to match the 1st, 2nd, 3rd and 10th number as defined earlier is correct.