Associated Topics || Dr. Math Home || Search Dr. Math

### Finding a Rule for a Sequence

```Date: 07/24/2003 at 13:50:59
From: John
Subject: Lots of trouble on this one

I have to find the next number and it's a mystery to me.

1, 3, 11, 67, ?
```

```
Date: 07/25/2003 at 01:34:24
From: Doctor Greenie
Subject: Re: Lots of trouble on this one

Hi, John -

It is impossible to determine what THE next number is in this
sequence. Given ANY sequence of numbers, it is possible to develop
many different rules which produce that given sequence of numbers -
but those many different rules may well produce different "subsequent"
numbers. In problems like this, as the number of given numbers
increases, it becomes harder and harder to find a rule that fits all
the given numbers; but with only the first four numbers given, it is
comparatively easy to find a rule that works.

Here is one way to find a rule that will find the next number (and
subsequent numbers) in the sequence:

1  ==>  times 2,  plus 1  ==>  = 3
3  ==>  times 4, minus 1  ==>  = 11
11  ==>  times 6,  plus 1  ==>  = 67

And so the next number in the sequence will be

67  ==>  times 8, minus 1  ==>  = 535

However, as I have noted, this is only one possible answer to the
problem. It is quite possible to find completely different rules
that generate these first four given numbers but give very different
next numbers.

I hope this helps. Please write back if you have any further questions

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Sequences, Series

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search