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#1 2024-10-08 14:51:23

mathenjoyer
Novice
Registered: 2024-10-08
Posts: 4

Number sequence help

Have this sequence puzzle on a test, can anyone help guess the next number?

4, 6, 2, 8, 3, 9, ?

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#2 2024-10-08 14:52:24

mathenjoyer
Novice
Registered: 2024-10-08
Posts: 4

Re: Number sequence help

Never mind, I got the answer, it's 1.5
Was a tricky one because I thought it would be an integer solution but it's not!

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#3 2024-10-09 06:01:00

Bob
Administrator
Registered: 2010-06-20
Posts: 10,610

Re: Number sequence help

hi mathenjoyer

Welcome to the forum!

Well I'm glad you found an answer.  I cannot! So how about helping me out here. dizzy Where did 1.5 come from?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2024-10-09 11:26:25

mathenjoyer
Novice
Registered: 2024-10-08
Posts: 4

Re: Number sequence help

9 / 6 = 1.5!!

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#5 2024-10-09 11:38:46

mathenjoyer
Novice
Registered: 2024-10-08
Posts: 4

Re: Number sequence help

Thanks for the warm welcome smile

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#6 2024-10-09 18:53:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,868

Re: Number sequence help

mathenjoyer wrote:

9 / 6 = 1.5!!

I think that 9 / 6 follows the correct strategy, but is incorrect because of a small error.

...unless I'm wrong! big_smile

Last edited by phrontister (2024-10-09 21:44:28)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#7 2024-10-10 00:36:34

Bob
Administrator
Registered: 2010-06-20
Posts: 10,610

Re: Number sequence help

mathenjoyer wrote:

9 / 6 = 1.5!!

Assume I'm really stupid. shame Please explain what the term to term rule is that generates this sequence. Thanks. smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#8 2024-10-10 01:20:50

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,868

Re: Number sequence help

Hi Bob;

Here's my method...but with a different result from mathenjoyer's:


#    Term







The bold numbers are a sequence of 6 numbers from 2 to 7, and the operators used are the repeating sequence + ÷ × – .   

I say 'repeating sequence', as the 5th term repeats the '+' used in the 1st term....from which it follows that the 6th term would use the '÷' from the 2nd term.

Last edited by phrontister (2024-10-10 22:36:38)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#9 2024-10-10 20:58:15

Bob
Administrator
Registered: 2010-06-20
Posts: 10,610

Re: Number sequence help

(1,4) (2,6) (3,2) (4,8) (5,3) (6,9)

bobbym once pointed out that you can always fit a function to any set of six points.

To be a 'solution' there has to be sufficient evidence from the given numbers to find a unique rule that will allow you to determine the next number(s).

I'm impressed with your answer phro. I'd never have got that.  But what is the rule that generates 1.5 as the next. I still cannot see it.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#10 2024-10-11 02:39:38

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,868

Re: Number sequence help

Hi Bob;

To be a 'solution' there has to be sufficient evidence from the given numbers to find a unique rule that will allow you to determine the next number(s).

Expressing my method isn't as easy as I'd hoped, but here goes (and I'm sorry, I don't know how to do non-LaTeX subscripts here on MIF):

Rule: Term 1 (t1) = 4, and subsequent terms (t2, t3, etc) follow the [+1] incrementing form { t2 = t1 + t2's term position }, with arithmetic operators for the respective terms being assigned from the repeating sequence { + / * – } (starting with '+' for t2).

Here's my demonstration worksheet for the first 9 terms (note that t6's operator begins the first repeat of the operator sequence):

FaYqU2vl.jpg

As you can see from the formulas in column H, calculations for terms after t1 are done entirely in column G. The other columns explain the calculations.

I'd never have got that.

I thought the same about my initial efforts, but then started again with an Excel spreadsheet to help organise & lay out my thoughts.

Light dawned while working out relationships between the adjacent given terms in column G and the various possible ways in which to arrive at each next term. That led to discovering the use of the 4 arithmetic operators, followed by recognising that the group of 4 operators was a repeating sequence. 

mathenjoyer wrote:

9 / 6 = 1.5!!

mathenjoyer wrote:

Never mind, I got the answer, it's 1.5

I'd really like to know the rule to get that answer! dizzy

Last edited by phrontister (2024-11-07 02:35:40)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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