SOLUTION: what should be the next number in this sequence: 4,14,14,1,5,2,1,9,3,___ 5,15,18,14,16,6,24,10,11,___

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Question 1184236: what should be the next number in this sequence:
4,14,14,1,5,2,1,9,3,___
5,15,18,14,16,6,24,10,11,___
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
4,14,14,1,5,2,1,9,3,___

Start with 4.

Add 10, get 14.
Add 0, get 14.
Subtract 13, get 1.
Add 4, get 5.
Subtract 3, get 2.
Subtract 1, get 1,
Add 8, get 9.
Subtract 6, get 3.

Now start over and do the same things. 

Add 10, get 13.
Add 0, get 13.
Subtract 13, get 0.
Add 4, get 4.
Subtract 3, get 1.
Subtract 1, get 0.
Add 8, get 8.
Subtract 6, get 2.

The sequence goes like this:

4, 14, 14, 1, 5, 2, 1, 9, 3, 13, 13, 0, 4, 1, 0, 8, 2, 
   12, 12, -1, 3, 0, -1, 7, 1, 11, 11, -2, 2, -1, -2, 6, 0, 
   10, 10, -3, 1, -2, -3, 5, -1, ...

Keep starting over, doing those same things over and over.  That's the pattern.

----------------------------------------------

5,15,18,14,16,6,24,10,11,___

Start with 5.

Add 10, get 15.
Add 3, get 18.
Subtract 4, get 14.
Add 2, get 16,
Subtract 10, get 6.
Add 18, get 24.
Subtract 14, get 10.
Add 1, get 11.

Now start over and do the same things. 

Add 10, get 21.
Add 3, get 24.
Subtract 4, get 20.
Add 2, get 22,
Subtract 10, get 12.
Add 18, get 30.
Subtract 14, get 16.
Add 1, get 17.

The sequence goes like this:

5, 15, 18, 14, 16, 6, 24, 10, 11, 
   21, 24, 20, 22, 12, 30, 16, 17, 
   27, 30, 26, 28, 18, 36, 22, 23, 
   33, 36, 32, 34, 24, 42, 28, 29, 
   39, 42, 38, 40, 30, 48, 34, 35, ...

Keep starting over, doing those same things over and over.  That's the pattern.

Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


There is no way to know the next number in either of these sequences, or in ANY problem where a sequence of numbers is given without any information about what type of sequence it is.

In both of these sequences, ANY next number will make a valid sequence.

Any problem like this must be considered a puzzle rather than a math problem.

Presumably the author of this problem had logical patterns in mind when producing each of these sequences. But in both of these cases (as in ANY similar problems) there are other logical patterns that produce the given numbers but produce different next numbers.

Finally, it is absurd to simply look at the differences between successive terms in the 9 given numbers and say "that's the pattern".
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