What will be the next term in this mathematical sequence?

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3














What will be next in this series?
$$0, 6, 24, 60, 120, 210, ...$$
I've tried it and noticed that the numbers are multiples of six. But I couldn't make a relation between them.










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  • the OEIS has three potential answers to this question.
    – Don Thousand
    Dec 25 '18 at 16:32















3














What will be next in this series?
$$0, 6, 24, 60, 120, 210, ...$$
I've tried it and noticed that the numbers are multiples of six. But I couldn't make a relation between them.










share|improve this question























  • the OEIS has three potential answers to this question.
    – Don Thousand
    Dec 25 '18 at 16:32













3












3








3







What will be next in this series?
$$0, 6, 24, 60, 120, 210, ...$$
I've tried it and noticed that the numbers are multiples of six. But I couldn't make a relation between them.










share|improve this question















What will be next in this series?
$$0, 6, 24, 60, 120, 210, ...$$
I've tried it and noticed that the numbers are multiples of six. But I couldn't make a relation between them.







mathematics pattern calculation-puzzle






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edited Dec 25 '18 at 9:46









Rand al'Thor

69k14229462




69k14229462










asked Dec 25 '18 at 9:36









Gurbir Singh

1193




1193











  • the OEIS has three potential answers to this question.
    – Don Thousand
    Dec 25 '18 at 16:32
















  • the OEIS has three potential answers to this question.
    – Don Thousand
    Dec 25 '18 at 16:32















the OEIS has three potential answers to this question.
– Don Thousand
Dec 25 '18 at 16:32




the OEIS has three potential answers to this question.
– Don Thousand
Dec 25 '18 at 16:32










4 Answers
4






active

oldest

votes


















1














It seems like




sum of digit series

f(n)=n*sumOfDigits(n-1)*sumOfDigits(n+1)




example:-




f(1)=1*sumOfDigits(1-1)*sumOfDigits(1+1) = 1*0*2 = 0

f(2)=2*sumOfDigits(2-1)*sumOfDigits(2+1) = 2*1*3 = 6

f(3)=3*sumOfDigits(3-1)*sumOfDigits(3+1) = 3*2*4 = 24

f(4)=4*sumOfDigits(4-1)*sumOfDigits(4+1) = 4*3*5 = 60

f(5)=5*sumOfDigits(5-1)*sumOfDigits(5+1) = 5*4*6 = 120

f(6)=6*sumOfDigits(6-1)*sumOfDigits(6+1) = 6*5*7 = 210




Answer:-




f(7)=7*sumOfDigits(7-1)*sumOfDigits(7+1) = 7*6*8 = 336







share|improve this answer
















  • 2




    That's copying my solution
    – TheSimpliFire
    Dec 28 '18 at 13:27


















8














It seems like a




cube series.




Namely,




cube of 1 is 1 then 1 - 1 = 0

cube of 2 is 8 then 8 - 2 = 6

cube of 3 is 27 then 27 - 3 = 24

cube of 4 is 64 then 64 - 4 = 60

cube of 5 is 125 then 125 - 5 = 120

cube of 6 is 216 then 216 - 6 = 210

cube of 7 is 343 then 343 - 7 = 336







share|improve this answer






















  • Thanks. Nice explanation.
    – Gurbir Singh
    Dec 25 '18 at 11:26


















4















  • Take differences between terms:




    $6, 18, 36, 60, 90, ...$





  • Notice that these are




    $6$ times the triangular numbers $1, 3, 6, 12, 15, ...$




So the next difference should be




$6times 21 = 126$




and the next term should be




$210+126=336$.







share|improve this answer


















  • 2




    The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
    – athin
    Dec 25 '18 at 11:07


















4














Simple Answer:




The $n$th term is $n(n-1)(n+1)$ and thus the required one is the seventh term giving an answer of $$7(6)(8)=336.$$







share|improve this answer




















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    4 Answers
    4






    active

    oldest

    votes








    4 Answers
    4






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1














    It seems like




    sum of digit series

    f(n)=n*sumOfDigits(n-1)*sumOfDigits(n+1)




    example:-




    f(1)=1*sumOfDigits(1-1)*sumOfDigits(1+1) = 1*0*2 = 0

    f(2)=2*sumOfDigits(2-1)*sumOfDigits(2+1) = 2*1*3 = 6

    f(3)=3*sumOfDigits(3-1)*sumOfDigits(3+1) = 3*2*4 = 24

    f(4)=4*sumOfDigits(4-1)*sumOfDigits(4+1) = 4*3*5 = 60

    f(5)=5*sumOfDigits(5-1)*sumOfDigits(5+1) = 5*4*6 = 120

    f(6)=6*sumOfDigits(6-1)*sumOfDigits(6+1) = 6*5*7 = 210




    Answer:-




    f(7)=7*sumOfDigits(7-1)*sumOfDigits(7+1) = 7*6*8 = 336







    share|improve this answer
















    • 2




      That's copying my solution
      – TheSimpliFire
      Dec 28 '18 at 13:27















    1














    It seems like




    sum of digit series

    f(n)=n*sumOfDigits(n-1)*sumOfDigits(n+1)




    example:-




    f(1)=1*sumOfDigits(1-1)*sumOfDigits(1+1) = 1*0*2 = 0

    f(2)=2*sumOfDigits(2-1)*sumOfDigits(2+1) = 2*1*3 = 6

    f(3)=3*sumOfDigits(3-1)*sumOfDigits(3+1) = 3*2*4 = 24

    f(4)=4*sumOfDigits(4-1)*sumOfDigits(4+1) = 4*3*5 = 60

    f(5)=5*sumOfDigits(5-1)*sumOfDigits(5+1) = 5*4*6 = 120

    f(6)=6*sumOfDigits(6-1)*sumOfDigits(6+1) = 6*5*7 = 210




    Answer:-




    f(7)=7*sumOfDigits(7-1)*sumOfDigits(7+1) = 7*6*8 = 336







    share|improve this answer
















    • 2




      That's copying my solution
      – TheSimpliFire
      Dec 28 '18 at 13:27













    1












    1








    1






    It seems like




    sum of digit series

    f(n)=n*sumOfDigits(n-1)*sumOfDigits(n+1)




    example:-




    f(1)=1*sumOfDigits(1-1)*sumOfDigits(1+1) = 1*0*2 = 0

    f(2)=2*sumOfDigits(2-1)*sumOfDigits(2+1) = 2*1*3 = 6

    f(3)=3*sumOfDigits(3-1)*sumOfDigits(3+1) = 3*2*4 = 24

    f(4)=4*sumOfDigits(4-1)*sumOfDigits(4+1) = 4*3*5 = 60

    f(5)=5*sumOfDigits(5-1)*sumOfDigits(5+1) = 5*4*6 = 120

    f(6)=6*sumOfDigits(6-1)*sumOfDigits(6+1) = 6*5*7 = 210




    Answer:-




    f(7)=7*sumOfDigits(7-1)*sumOfDigits(7+1) = 7*6*8 = 336







    share|improve this answer












    It seems like




    sum of digit series

    f(n)=n*sumOfDigits(n-1)*sumOfDigits(n+1)




    example:-




    f(1)=1*sumOfDigits(1-1)*sumOfDigits(1+1) = 1*0*2 = 0

    f(2)=2*sumOfDigits(2-1)*sumOfDigits(2+1) = 2*1*3 = 6

    f(3)=3*sumOfDigits(3-1)*sumOfDigits(3+1) = 3*2*4 = 24

    f(4)=4*sumOfDigits(4-1)*sumOfDigits(4+1) = 4*3*5 = 60

    f(5)=5*sumOfDigits(5-1)*sumOfDigits(5+1) = 5*4*6 = 120

    f(6)=6*sumOfDigits(6-1)*sumOfDigits(6+1) = 6*5*7 = 210




    Answer:-




    f(7)=7*sumOfDigits(7-1)*sumOfDigits(7+1) = 7*6*8 = 336








    share|improve this answer












    share|improve this answer



    share|improve this answer










    answered Dec 27 '18 at 13:03









    Vivek Kundariya

    263




    263







    • 2




      That's copying my solution
      – TheSimpliFire
      Dec 28 '18 at 13:27












    • 2




      That's copying my solution
      – TheSimpliFire
      Dec 28 '18 at 13:27







    2




    2




    That's copying my solution
    – TheSimpliFire
    Dec 28 '18 at 13:27




    That's copying my solution
    – TheSimpliFire
    Dec 28 '18 at 13:27











    8














    It seems like a




    cube series.




    Namely,




    cube of 1 is 1 then 1 - 1 = 0

    cube of 2 is 8 then 8 - 2 = 6

    cube of 3 is 27 then 27 - 3 = 24

    cube of 4 is 64 then 64 - 4 = 60

    cube of 5 is 125 then 125 - 5 = 120

    cube of 6 is 216 then 216 - 6 = 210

    cube of 7 is 343 then 343 - 7 = 336







    share|improve this answer






















    • Thanks. Nice explanation.
      – Gurbir Singh
      Dec 25 '18 at 11:26















    8














    It seems like a




    cube series.




    Namely,




    cube of 1 is 1 then 1 - 1 = 0

    cube of 2 is 8 then 8 - 2 = 6

    cube of 3 is 27 then 27 - 3 = 24

    cube of 4 is 64 then 64 - 4 = 60

    cube of 5 is 125 then 125 - 5 = 120

    cube of 6 is 216 then 216 - 6 = 210

    cube of 7 is 343 then 343 - 7 = 336







    share|improve this answer






















    • Thanks. Nice explanation.
      – Gurbir Singh
      Dec 25 '18 at 11:26













    8












    8








    8






    It seems like a




    cube series.




    Namely,




    cube of 1 is 1 then 1 - 1 = 0

    cube of 2 is 8 then 8 - 2 = 6

    cube of 3 is 27 then 27 - 3 = 24

    cube of 4 is 64 then 64 - 4 = 60

    cube of 5 is 125 then 125 - 5 = 120

    cube of 6 is 216 then 216 - 6 = 210

    cube of 7 is 343 then 343 - 7 = 336







    share|improve this answer














    It seems like a




    cube series.




    Namely,




    cube of 1 is 1 then 1 - 1 = 0

    cube of 2 is 8 then 8 - 2 = 6

    cube of 3 is 27 then 27 - 3 = 24

    cube of 4 is 64 then 64 - 4 = 60

    cube of 5 is 125 then 125 - 5 = 120

    cube of 6 is 216 then 216 - 6 = 210

    cube of 7 is 343 then 343 - 7 = 336








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited Dec 25 '18 at 13:40









    Omega Krypton

    2,5101227




    2,5101227










    answered Dec 25 '18 at 11:11









    Shailendra Sharma

    1803




    1803











    • Thanks. Nice explanation.
      – Gurbir Singh
      Dec 25 '18 at 11:26
















    • Thanks. Nice explanation.
      – Gurbir Singh
      Dec 25 '18 at 11:26















    Thanks. Nice explanation.
    – Gurbir Singh
    Dec 25 '18 at 11:26




    Thanks. Nice explanation.
    – Gurbir Singh
    Dec 25 '18 at 11:26











    4















    • Take differences between terms:




      $6, 18, 36, 60, 90, ...$





    • Notice that these are




      $6$ times the triangular numbers $1, 3, 6, 12, 15, ...$




    So the next difference should be




    $6times 21 = 126$




    and the next term should be




    $210+126=336$.







    share|improve this answer


















    • 2




      The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
      – athin
      Dec 25 '18 at 11:07















    4















    • Take differences between terms:




      $6, 18, 36, 60, 90, ...$





    • Notice that these are




      $6$ times the triangular numbers $1, 3, 6, 12, 15, ...$




    So the next difference should be




    $6times 21 = 126$




    and the next term should be




    $210+126=336$.







    share|improve this answer


















    • 2




      The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
      – athin
      Dec 25 '18 at 11:07













    4












    4








    4







    • Take differences between terms:




      $6, 18, 36, 60, 90, ...$





    • Notice that these are




      $6$ times the triangular numbers $1, 3, 6, 12, 15, ...$




    So the next difference should be




    $6times 21 = 126$




    and the next term should be




    $210+126=336$.







    share|improve this answer















    • Take differences between terms:




      $6, 18, 36, 60, 90, ...$





    • Notice that these are




      $6$ times the triangular numbers $1, 3, 6, 12, 15, ...$




    So the next difference should be




    $6times 21 = 126$




    and the next term should be




    $210+126=336$.








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited Dec 25 '18 at 12:10









    Omega Krypton

    2,5101227




    2,5101227










    answered Dec 25 '18 at 9:46









    Rand al'Thor

    69k14229462




    69k14229462







    • 2




      The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
      – athin
      Dec 25 '18 at 11:07












    • 2




      The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
      – athin
      Dec 25 '18 at 11:07







    2




    2




    The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
    – athin
    Dec 25 '18 at 11:07




    The multiplication on the third spoiler is incorrect. And also, the sequence can be found on the OEIS as a nice formula: oeis.org/A007531
    – athin
    Dec 25 '18 at 11:07











    4














    Simple Answer:




    The $n$th term is $n(n-1)(n+1)$ and thus the required one is the seventh term giving an answer of $$7(6)(8)=336.$$







    share|improve this answer

























      4














      Simple Answer:




      The $n$th term is $n(n-1)(n+1)$ and thus the required one is the seventh term giving an answer of $$7(6)(8)=336.$$







      share|improve this answer























        4












        4








        4






        Simple Answer:




        The $n$th term is $n(n-1)(n+1)$ and thus the required one is the seventh term giving an answer of $$7(6)(8)=336.$$







        share|improve this answer












        Simple Answer:




        The $n$th term is $n(n-1)(n+1)$ and thus the required one is the seventh term giving an answer of $$7(6)(8)=336.$$








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered Dec 25 '18 at 13:45









        TheSimpliFire

        2,150532




        2,150532



























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