Math Is Fun Forum

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, ?

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!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,589

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. Where did 1.5 come from?

Bob

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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

mathenjoyer

Novice

Registered: 2024-10-08

Posts: 4

Re: Number sequence help

9 / 6 = 1.5!!

mathenjoyer

Novice

Registered: 2024-10-08

Posts: 4

Re: Number sequence help

Thanks for the warm welcome

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,866

Re: Number sequence help

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!

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

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"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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,589

Re: Number sequence help

9 / 6 = 1.5!!

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

Bob

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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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,866

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)

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"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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,589

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

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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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,866

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:

Let 't1' (sorry, I don't know how to do non-LaTeX subscripts here) be the 1st term number and 'n1' its position in the list of terms. Subsequent term numbers are t2, t3, t4, t5,... etc, their respective positions being n2, n3, n4, n5,...etc.
4 arithmetic operators ( + / * – ) are used...individually, and in that particular order, being a repeating sequence.

After t1, the next 4 terms are determined by the formulas t1 + n2, t2 / n3, t3 * n4, and t5 – n5, where terms (t) and term positions (n) increment by 1 and the 4 arithmetic operators are used in order.

Subsequent terms are also determined by this pattern, with the operator sequence repeating after each completed sequence.

No doubt that can be expressed much better/simpler!

Here's my worksheet for the first 9 terms:

I set it out a bit differently from Post #8, but basically follows the same idea.

As you can see from the formulas in column G, all calculations are done in column F. The other columns are there just for visual explanation.

I'd never have got that.

I thought the same about my initial efforts, but then started again with an Excel spreadsheet this time to help with clarity.

Light dawned while working out relationships between adjacent terms in column F and the various ways in which to arrive at each next given 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. 

But what is the rule that generates 1.5 as the next. I still cannot see it.

I can't see it either...which is why I'm wondering if that's an error (as I said in Post #6):

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

The "correct strategy" I referred to there is the division, which my method also uses for that term. The "small error" refers to the 6 (my method has 7).

If mathenjoyer's 9 / 6 = 1.5 answer is correct, I'm stuck!

Last edited by phrontister (2024-10-13 08:01:10)

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"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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,866

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).

Here's an attempt at a simpler rule than the one in my previous post:

Rule: Term 1 (t1) = 4, and subsequent terms (t2, t3, etc) follow the incrementing form t2 = t1 + t2's position in the terms list. Each term's arithmetic operator comes from the repeating ordered group of 4 operators  + / * – , with t2's being '+', t5's '–', t6's '+', etc.

Here's my worksheet for the first 9 terms:

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 what's happening in each calculation.

Last edited by phrontister (Today 20:11:12)

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"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