What number comes next in this sequence?
$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.
What comes next? The answer is $-25$, but why?
sequences-and-series pattern-recognition
asked Nov 24 at 21:49
stackofhay42
1696
add a comment |
$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.
What comes next? The answer is $-25$, but why?
sequences-and-series pattern-recognition
asked Nov 24 at 21:49
stackofhay42
1696
16
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
3
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
1
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11
add a comment |
$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.
What comes next? The answer is $-25$, but why?
sequences-and-series pattern-recognition
asked Nov 24 at 21:49
stackofhay42
1696
$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.
What comes next? The answer is $-25$, but why?
sequences-and-series pattern-recognition
sequences-and-series pattern-recognition
asked Nov 24 at 21:49
stackofhay42
1696
asked Nov 24 at 21:49
stackofhay42
1696
asked Nov 24 at 21:49
stackofhay42
1696
asked Nov 24 at 21:49
stackofhay42
1696
asked Nov 24 at 21:49
stackofhay42
1696
1696
16
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
3
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
1
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11
add a comment |
16
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
3
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
1
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11
16
16
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
3
3
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
1
1
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11
add a comment |
3 Answers
3
active
oldest
votes
Break up the sequence into the even ordered terms and odd ordered.
answered Nov 24 at 21:53
TurlocTheRed
818311
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
add a comment |
- Firs observation, first term and second term add up to 19, third and fourth add to 20, fifth and sixth add to 21 and so on..
According to that, the the next number is $49+x = 24 implies x = -25$
- Second observation, second and third terms add to 28, the fourth and fifth add to 29 and so on...
Therefore, you can generate the next number using these two observations anywhere in the sequence.
I know this is not the best way to predict the next number. However, it is not a bad try.
:)
answered Nov 24 at 21:59
Maged Saeed
847316
add a comment |
As a general rule, the simplest kind of sequences of numbers are linear recurrence sequences. It is a matter of finding the recurrence relation. Using the first $10$ terms of the sequence, and linear algebra, the generating function appears to be
$$ A(x) := frac{-23 x^4 + 5 x^3 + 15 x^2 + 4 x}{(x^2 - 1)^2} = 4 x + 15x^2 + 13x^3 +dots $$
with the $11$th term $49$ being consistent with the generating function.
The $12$th term is then $-25$ as you stated. The polynomial numerator and denominator coefficients can be found using linear algebra in the general case. In your case, by looking at every other term, you can find that they are both arithmetic progressions with constant differences $9$ and $-8$.
answered Nov 25 at 3:21
Somos
12.8k11034
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Break up the sequence into the even ordered terms and odd ordered.
answered Nov 24 at 21:53
TurlocTheRed
818311
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
add a comment |
Break up the sequence into the even ordered terms and odd ordered.
answered Nov 24 at 21:53
TurlocTheRed
818311
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
add a comment |
Break up the sequence into the even ordered terms and odd ordered.
answered Nov 24 at 21:53
TurlocTheRed
818311
Break up the sequence into the even ordered terms and odd ordered.
answered Nov 24 at 21:53
TurlocTheRed
818311
answered Nov 24 at 21:53
TurlocTheRed
818311
answered Nov 24 at 21:53
TurlocTheRed
818311
answered Nov 24 at 21:53
TurlocTheRed
818311
818311
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
add a comment |
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
2
2
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
Wow! I was looking for some very complicated patterns, and it is actually so easy.
– Mark
Nov 24 at 21:55
add a comment |
- Firs observation, first term and second term add up to 19, third and fourth add to 20, fifth and sixth add to 21 and so on..
According to that, the the next number is $49+x = 24 implies x = -25$
- Second observation, second and third terms add to 28, the fourth and fifth add to 29 and so on...
Therefore, you can generate the next number using these two observations anywhere in the sequence.
I know this is not the best way to predict the next number. However, it is not a bad try.
:)
answered Nov 24 at 21:59
Maged Saeed
847316
add a comment |
- Firs observation, first term and second term add up to 19, third and fourth add to 20, fifth and sixth add to 21 and so on..
According to that, the the next number is $49+x = 24 implies x = -25$
- Second observation, second and third terms add to 28, the fourth and fifth add to 29 and so on...
Therefore, you can generate the next number using these two observations anywhere in the sequence.
I know this is not the best way to predict the next number. However, it is not a bad try.
:)
answered Nov 24 at 21:59
Maged Saeed
847316
add a comment |
- Firs observation, first term and second term add up to 19, third and fourth add to 20, fifth and sixth add to 21 and so on..
According to that, the the next number is $49+x = 24 implies x = -25$
- Second observation, second and third terms add to 28, the fourth and fifth add to 29 and so on...
Therefore, you can generate the next number using these two observations anywhere in the sequence.
I know this is not the best way to predict the next number. However, it is not a bad try.
:)
answered Nov 24 at 21:59
Maged Saeed
847316
- Firs observation, first term and second term add up to 19, third and fourth add to 20, fifth and sixth add to 21 and so on..
According to that, the the next number is $49+x = 24 implies x = -25$
- Second observation, second and third terms add to 28, the fourth and fifth add to 29 and so on...
Therefore, you can generate the next number using these two observations anywhere in the sequence.
I know this is not the best way to predict the next number. However, it is not a bad try.
:)
answered Nov 24 at 21:59
Maged Saeed
847316
edited Nov 24 at 22:21
answered Nov 24 at 21:59
Maged Saeed
847316
answered Nov 24 at 21:59
Maged Saeed
847316
answered Nov 24 at 21:59
Maged Saeed
847316
847316
add a comment |
add a comment |
As a general rule, the simplest kind of sequences of numbers are linear recurrence sequences. It is a matter of finding the recurrence relation. Using the first $10$ terms of the sequence, and linear algebra, the generating function appears to be
$$ A(x) := frac{-23 x^4 + 5 x^3 + 15 x^2 + 4 x}{(x^2 - 1)^2} = 4 x + 15x^2 + 13x^3 +dots $$
with the $11$th term $49$ being consistent with the generating function.
The $12$th term is then $-25$ as you stated. The polynomial numerator and denominator coefficients can be found using linear algebra in the general case. In your case, by looking at every other term, you can find that they are both arithmetic progressions with constant differences $9$ and $-8$.
answered Nov 25 at 3:21
Somos
12.8k11034
add a comment |
As a general rule, the simplest kind of sequences of numbers are linear recurrence sequences. It is a matter of finding the recurrence relation. Using the first $10$ terms of the sequence, and linear algebra, the generating function appears to be
$$ A(x) := frac{-23 x^4 + 5 x^3 + 15 x^2 + 4 x}{(x^2 - 1)^2} = 4 x + 15x^2 + 13x^3 +dots $$
with the $11$th term $49$ being consistent with the generating function.
The $12$th term is then $-25$ as you stated. The polynomial numerator and denominator coefficients can be found using linear algebra in the general case. In your case, by looking at every other term, you can find that they are both arithmetic progressions with constant differences $9$ and $-8$.
answered Nov 25 at 3:21
Somos
12.8k11034
add a comment |
As a general rule, the simplest kind of sequences of numbers are linear recurrence sequences. It is a matter of finding the recurrence relation. Using the first $10$ terms of the sequence, and linear algebra, the generating function appears to be
$$ A(x) := frac{-23 x^4 + 5 x^3 + 15 x^2 + 4 x}{(x^2 - 1)^2} = 4 x + 15x^2 + 13x^3 +dots $$
with the $11$th term $49$ being consistent with the generating function.
The $12$th term is then $-25$ as you stated. The polynomial numerator and denominator coefficients can be found using linear algebra in the general case. In your case, by looking at every other term, you can find that they are both arithmetic progressions with constant differences $9$ and $-8$.
answered Nov 25 at 3:21
Somos
12.8k11034
As a general rule, the simplest kind of sequences of numbers are linear recurrence sequences. It is a matter of finding the recurrence relation. Using the first $10$ terms of the sequence, and linear algebra, the generating function appears to be
$$ A(x) := frac{-23 x^4 + 5 x^3 + 15 x^2 + 4 x}{(x^2 - 1)^2} = 4 x + 15x^2 + 13x^3 +dots $$
with the $11$th term $49$ being consistent with the generating function.
The $12$th term is then $-25$ as you stated. The polynomial numerator and denominator coefficients can be found using linear algebra in the general case. In your case, by looking at every other term, you can find that they are both arithmetic progressions with constant differences $9$ and $-8$.
answered Nov 25 at 3:21
Somos
12.8k11034
answered Nov 25 at 3:21
Somos
12.8k11034
answered Nov 25 at 3:21
Somos
12.8k11034
answered Nov 25 at 3:21
Somos
12.8k11034
12.8k11034
add a comment |
add a comment |
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16
My answer is 42. The reason is that I like the number 42. And there is no one who can prove me wrong. That being said, if I were to try to read the mind of whoever made this problem, I would look at every other term.
– Arthur
Nov 24 at 21:52
3
Any finite sequence of integers can be continued any way you like. Sometimes there are patterns that suggest that one continuation is more natural than another. I see no such pattern here. If you [edit' the question to tell us where the sequence comes from we may be able to hlep. Otherwise the question will probably be closed.
– Ethan Bolker
Nov 24 at 21:53
1
wolframalpha.com/input/…
– AccidentalFourierTransform
Nov 25 at 0:11