# Number sequence

73 replies to this topic

### #18 Boerseun

Boerseun

Phantom Cow of Justice

• Members
• 6062 posts

Posted 15 September 2006 - 12:05 AM

I will tell you if its 110 by tomorrow when he answers my email. Oh and big dog It doesnt double 4 more times since 50 is not two times 30. Boerseun how did you get 110 since the method is more important than the answer

It seems as if the difference in the sum for the preceding 1-digit numbers are 1. i.e., you have to add 1 to 1+2+4=7(+1) = 8, then to get to 30 you have to add another 1, (1)+1+2+4+8+15=30. Then, for some reason, the difference becomes 10 to the negative. And seeing as the initial statement said that the next number in the sequence must be less than 150, I assume that there will simply be another digit added, and also to the negative, i.e. the sum of all the numbers minus 100.

You're right - I am by no stretch of the imagination a mathematician.

### #19 Jay-qu

Jay-qu

Ancora Imparo

• Members
• 6340 posts

Posted 15 September 2006 - 01:34 AM

It seems as if the difference in the sum for the preceding 1-digit numbers are 1. i.e., you have to add 1 to 1+2+4=7(+1) = 8, then to get to 30 you have to add another 1, (1)+1+2+4+8+15=30. Then, for some reason, the difference becomes 10 to the negative. And seeing as the initial statement said that the next number in the sequence must be less than 150, I assume that there will simply be another digit added, and also to the negative, i.e. the sum of all the numbers minus 100.

You're right - I am by no stretch of the imagination a mathematician.

I was going along with this patturn aswell.. somehow ended up getting 100 awaiting an answer

### #20 CraigD

CraigD

Creating

• 8034 posts

Posted 15 September 2006 - 12:16 PM

149.

It’s is the next (n=9) number given by
$F(n) = - \frac{29}{5040} n^8 + \frac{277}{1260} n^7 - \frac{1267}{360} n^6 + \frac{1381}{45} n^5 - \frac{114083}{720} n^4 + \frac{88639}{180} n^3 - \frac{374021}{420} n^2 + \frac{88846}{105} n – 361$
, which give 1, 2, 4, 8, 15, 30, 50, 100 as its first 8 numbers.

The next (N=10) number is -494, and they keep getting more negative from there.

I’m pretty sure this isn’t what anto’s teacher had in mind. I could have as easily chosen any number (I assume) greater than 100, but less than 150. I got frustrated trying to figure out a simple rule to generate the sequence, so found a generating polynomial that fit the given conditions. Not something that many 5th grade students would do, but at least it’s easy to explain (and generate LaTex for).

As the saying goes, when the only tool you have is a hammer (Any forward difference formula, in this case), everything looks like a nail!

I’m not giving up on the challenge of finding the right answer. Could we have another clue, such as the number that comes after (n=10) the one we’re to find?

### #21 Boerseun

Boerseun

Phantom Cow of Justice

• Members
• 6062 posts

Posted 15 September 2006 - 01:29 PM

That's to say if there actually is an answer!
Checked the sequence on Yahoo, and there are quite a number of links, and ALL of them saying they have the sequence but nobody knows the next number!

They're havin' us on!

There is no next number! It's a hoax! Somewhere in the middle of dataland some first-year student's laughing his *** off...

Checkit...

### #22 TheBigDog

TheBigDog

Doing the Impossible

• Members
• 4095 posts

Posted 15 September 2006 - 01:42 PM

I played with this a different way looking for patterns that a 5th grader might find. And doing the basic math correctly this time

I broke the sequence into pairs. And the pairs into a pattern as follows...

1 * 1 = 1
1 * 2 = 2

2 * 2 = 4
2 * 4 = 8

3 * 5 = 15
3 * 10 = 30

5 * 10 = 50
5 * 20 = 100

I have no idea how the transition from blue to green happens. But ignoring that and dealing with the other pairs I get this semi pattern.

Primes (plue the number one) in the first column yeilds the next pair as...
7 * 20 = 140
7 * 40 = 280

The other one I am thinking of is Fibinocci which would make the next pair
8 * 20 = 160
8 * 40 = 320

But this does not fit the rule of being less than 150. And I am still no closer to explaining the transition from green to blue.

Bill
• Turtle likes this

### #23 Turtle

Turtle

Member

• Members
• 15452 posts

Posted 15 September 2006 - 01:44 PM

That's to say if there actually is an answer!
They're havin' us on!
Checkit...

I concur. On the other hand, this sequence is no have-on:
24, 30, 42 , 54, 66, 78, 102, 114, 138, 174, 186, 222, 258, 282...

I dare say that only those who already know the answer can provide the next element.

### #24 anto

anto

Thinking

• Members
• 36 posts

Posted 15 September 2006 - 01:46 PM

wow guys thanks for all the new answers Ill email my teacher right away. BTW he told me that their is definetely an answer. Oh and boerseum 110 is not the answer.

### #25 TheBigDog

TheBigDog

Doing the Impossible

• Members
• 4095 posts

Posted 15 September 2006 - 01:46 PM

I played with this a different way looking for patterns that a 5th grader might find. And doing the basic math correctly this time

I broke the sequence into pairs. And the pairs into a pattern as follows...

1 * 1 = 1
1 * 2 = 2

2 * 2 = 4
2 * 4 = 8

3 * 5 = 15
3 * 10 = 30

5 * 10 = 50
5 * 20 = 100

I have no idea how the transition from blue to green happens. But ignoring that and dealing with the other pairs I get this semi pattern.

Primes (plue the number one) in the first column yeilds the next pair as...
7 * 20 = 140
7 * 40 = 280

The other one I am thinking of is Fibinocci which would make the next pair
8 * 20 = 160
8 * 40 = 320

But this does not fit the rule of being less than 150. And I am still no closer to explaining the transition from green to blue.

Bill

If the transitions happen in a pattern the only one I see is +0, +1, +0... which would make the next one +1. So that would make the next number...
7 * 21 = 147
7 * 42 = 294

This fits all the rules. So my answer is 147

Bill

### #26 Turtle

Turtle

Member

• Members
• 15452 posts

Posted 15 September 2006 - 01:50 PM

wow guys thanks for all the new answers Ill email my teacher right away. BTW he told me that their is definetely an answer. Oh and boerseum 110 is not the answer.

Hey Anto, may I ask you to give your proff the sequence I just posted?
24, 30, 42 , 54, 66, 78, 102, 114, 138, 174, 186, 222, 258, 282...
There definately is an answer, and he definately doesn't know it. Thanks.

### #27 anto

anto

Thinking

• Members
• 36 posts

Posted 15 September 2006 - 01:54 PM

yeah definetely turtle I will, oh and b/c he gave us hints can you give him some?? Its only fair I guess.

Bill, great answer Ill let you know as soon as I can

### #28 Turtle

Turtle

Member

• Members
• 15452 posts

Posted 15 September 2006 - 01:59 PM

yeah definetely turtle I will, oh and b/c he gave us hints can you give him some?? Its only fair I guess.

Sure. The next element does not follow what appears to be the pattern of those listed.

### #29 anto

anto

Thinking

• Members
• 36 posts

Posted 15 September 2006 - 02:02 PM

hahaha that hint is quite ridiculous (no offense turle) lol b/c then whats the point if it doesnt follow a certain pattern then it could be any number..couldn't it? Oh and again, no offense intended with the word "ridiculous".

### #30 TheBigDog

TheBigDog

Doing the Impossible

• Members
• 4095 posts

Posted 15 September 2006 - 02:04 PM

Hey Anto, may I ask you to give your proff the sequence I just posted?
24, 30, 42 , 54, 66, 78, 102, 114, 138, 174, 186, 222, 258, 282...
There definately is an answer, and he definately doesn't know it. Thanks.

OOOO!!! OOO!!! Can I guess? Did we build a program that searched for these numbers? They look strangely familiar.

Bill

### #31 anto

anto

Thinking

• Members
• 36 posts

Posted 15 September 2006 - 02:09 PM

Just b/c I feel like it Ill give one of the answer I came up with..which of course was wrong, but I just want to share one of the ideas I had

1 2 4 8 15 30 50 100

1 2 4 7 15 20 50 differences between numbers

1 2 3 8 5 30 again differences

1 1 5 (-3) 25 yet again differences

0 4 (- 28 differences

4 (-12) 36

finally I found something ion common between the differences (need to multiply times negative three to get the next term) so multiplying by negative three and doing the math you get 125 which is of course, wrong

### #32 CraigD

CraigD

Creating

• 8034 posts

Posted 15 September 2006 - 05:07 PM

24, 30, 42 , 54, 66, 78, 102, 114, 138, 174, 186, 222, 258, 282...

Is the next in this sequence 318?

### #33 Turtle

Turtle

Member

• Members
• 15452 posts

Posted 15 September 2006 - 05:16 PM

Is the next in this sequence 318?

No Sir. (Confusing Hint: but 318 is in the list.)

### #34 anto

anto

Thinking

• Members
• 36 posts

Posted 15 September 2006 - 07:02 PM

Turtle is it 294?