Split from Numerical Sequence Brain Strain

Steven G

Steven G

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ref: https://www.freemathhelp.com/forum/threads/numerical-sequence-brain-strain.121120/#post-487240
tkhunny said:
No, in ALL cases there ARE infinitely many answers to such a question. This is what makes the exercise illogical; although it does give some practice in pattern recognition and various interpolation and extrapolation techniques.

In the case of your five specific problems, and the five specific answer from which to choose, one can construct a rule for ALL FIVE answers to fit ALL FIVE questions. It simply is not appropriate to suggest that a single answer necessarily applies to a single sequence.

Here's one of my favorite examples:

0
14
17
18
24
25
27
32
34
38
39
45
46
47
49
49
49
49
50

What's THE next number? What's THE rule?
Click to expand...
Randomness?
 
Last edited by a moderator:
tkhunny said:
No, in ALL cases there ARE infinitely many answers to such a question. This is what makes the exercise illogical; although it does give some practice in pattern recognition and various interpolation and extrapolation techniques.

In the case of your five specific problems, and the five specific answer from which to choose, one can construct a rule for ALL FIVE answers to fit ALL FIVE questions. It simply is not appropriate to suggest that a single answer necessarily applies to a single sequence.

Here's one of my favorite examples:

0
14
17
18
24
25
27
32
34
38
39
45
46
47
49
49
49
49
50

What's THE next number? What's THE rule?
Click to expand...
My favorite one is:

2, 4, 8, 16, 31, 57, .....
 
Jomo said:
If I learned one thing on this forum it is that there is a rule, well actually many many rules.
Click to expand...
Okay, it deserves more information. The next 5 values are 50, 50, 50, 50, 50.
 
Jomo said:
Oh boy, there you go again messing up. The last two numbers you listed should be 32 and 64. If only Sal had tutored you!
Click to expand...
Yes ... if only the sequence is an = 2^n

However, this sequence is more insidious......

In this case,

an = 1/24 * [(n+1)4 - 6(n+1)3 + 23(n+1)2 - 18(n+1) + 24]
 
To our lovely Super Moderator Subhotosh Khan: Can you please make a separate post for your problem. Thank you very much. If you keep this up I will have to tell Salman about you.
BTW, have a great day.
 
tkhunny said:
No, in ALL cases there ARE infinitely many answers to such a question. This is what makes the exercise illogical; although it does give some practice in pattern recognition and various interpolation and extrapolation techniques.

In the case of your five specific problems, and the five specific answers from which to choose, one can construct a rule for ALL FIVE answers to fit ALL FIVE questions. It simply is not appropriate to suggest that a single answer necessarily applies to a single sequence.

Here's one of my favorite examples:

0
14
17
18
24
25
27
32
34
38
39
45
46
47
49
49
49
49
50

What's THE next number? What's THE rule?
Click to expand...
I think it's 3 + 2i.

-Dan
 
Jomo said:
To our lovely Super Moderator Subhotosh Khan: Can you please make a separate post for your problem. Thank you very much. If you keep this up I will have to tell Salman about you.
BTW, have a great day.
Click to expand...
Wrong noun - it is an example of the question on the table - not a problem.

Although, I did put a question mark (?) at the end - it is a well-known example of follies of extrapolation (induction) - at least for us non-believer engineers.
 
Jomo said:
Is the answer more randomness?
Click to expand...
# of states/commonwealths in the USA, at each decade since 1790. Originally, I quit at 1950. There is a little fudging with 1870, as well. The next value won't exist for 10 years. Just an example of a "mathematical" list that has no "mathematical" basis.
 
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