What number comes next in this sequence?












2












$begingroup$


$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.



What comes next? The answer is $-25$, but why?






sequences-and-series pattern-recognition







share|cite|improve this question









$endgroup$








  • 16




    $begingroup$
    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.
    $endgroup$
    – Arthur
    Nov 24 '18 at 21:52








  • 4




    $begingroup$
    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.
    $endgroup$
    – Ethan Bolker
    Nov 24 '18 at 21:53






  • 1




    $begingroup$
    wolframalpha.com/input/…
    $endgroup$
    – AccidentalFourierTransform
    Nov 25 '18 at 0:11
















2












$begingroup$


$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.



What comes next? The answer is $-25$, but why?






sequences-and-series pattern-recognition







share|cite|improve this question









$endgroup$








  • 16




    $begingroup$
    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.
    $endgroup$
    – Arthur
    Nov 24 '18 at 21:52








  • 4




    $begingroup$
    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.
    $endgroup$
    – Ethan Bolker
    Nov 24 '18 at 21:53






  • 1




    $begingroup$
    wolframalpha.com/input/…
    $endgroup$
    – AccidentalFourierTransform
    Nov 25 '18 at 0:11














2












2








2


1



$begingroup$


$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.



What comes next? The answer is $-25$, but why?






sequences-and-series pattern-recognition







share|cite|improve this question









$endgroup$




$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$.



What comes next? The answer is $-25$, but why?






sequences-and-series pattern-recognition




sequences-and-series pattern-recognition






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 24 '18 at 21:49







user614735















  • 16




    $begingroup$
    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.
    $endgroup$
    – Arthur
    Nov 24 '18 at 21:52








  • 4




    $begingroup$
    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.
    $endgroup$
    – Ethan Bolker
    Nov 24 '18 at 21:53






  • 1




    $begingroup$
    wolframalpha.com/input/…
    $endgroup$
    – AccidentalFourierTransform
    Nov 25 '18 at 0:11














  • 16




    $begingroup$
    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.
    $endgroup$
    – Arthur
    Nov 24 '18 at 21:52








  • 4




    $begingroup$
    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.
    $endgroup$
    – Ethan Bolker
    Nov 24 '18 at 21:53






  • 1




    $begingroup$
    wolframalpha.com/input/…
    $endgroup$
    – AccidentalFourierTransform
    Nov 25 '18 at 0:11








16




16




$begingroup$
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.
$endgroup$
– Arthur
Nov 24 '18 at 21:52






$begingroup$
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.
$endgroup$
– Arthur
Nov 24 '18 at 21:52






4




4




$begingroup$
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.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:53




$begingroup$
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.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:53




1




1




$begingroup$
wolframalpha.com/input/…
$endgroup$
– AccidentalFourierTransform
Nov 25 '18 at 0:11




$begingroup$
wolframalpha.com/input/…
$endgroup$
– AccidentalFourierTransform
Nov 25 '18 at 0:11










3 Answers
3






active

oldest

votes


















14












$begingroup$

Break up the sequence into the even ordered terms and odd ordered.






share|cite|improve this answer









$endgroup$









  • 2




    $begingroup$
    Wow! I was looking for some very complicated patterns, and it is actually so easy.
    $endgroup$
    – Mark
    Nov 24 '18 at 21:55



















4












$begingroup$


  • 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.



:)






share|cite|improve this answer











$endgroup$





















    1












    $begingroup$

    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 $-8$.






    share|cite|improve this answer









    $endgroup$














      Your Answer








      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3012130%2fwhat-number-comes-next-in-this-sequence%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown
























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      14












      $begingroup$

      Break up the sequence into the even ordered terms and odd ordered.






      share|cite|improve this answer









      $endgroup$









      • 2




        $begingroup$
        Wow! I was looking for some very complicated patterns, and it is actually so easy.
        $endgroup$
        – Mark
        Nov 24 '18 at 21:55
















      14












      $begingroup$

      Break up the sequence into the even ordered terms and odd ordered.






      share|cite|improve this answer









      $endgroup$









      • 2




        $begingroup$
        Wow! I was looking for some very complicated patterns, and it is actually so easy.
        $endgroup$
        – Mark
        Nov 24 '18 at 21:55














      14












      14








      14





      $begingroup$

      Break up the sequence into the even ordered terms and odd ordered.






      share|cite|improve this answer









      $endgroup$



      Break up the sequence into the even ordered terms and odd ordered.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered Nov 24 '18 at 21:53









      TurlocTheRedTurlocTheRed

      1,034411




      1,034411








      • 2




        $begingroup$
        Wow! I was looking for some very complicated patterns, and it is actually so easy.
        $endgroup$
        – Mark
        Nov 24 '18 at 21:55














      • 2




        $begingroup$
        Wow! I was looking for some very complicated patterns, and it is actually so easy.
        $endgroup$
        – Mark
        Nov 24 '18 at 21:55








      2




      2




      $begingroup$
      Wow! I was looking for some very complicated patterns, and it is actually so easy.
      $endgroup$
      – Mark
      Nov 24 '18 at 21:55




      $begingroup$
      Wow! I was looking for some very complicated patterns, and it is actually so easy.
      $endgroup$
      – Mark
      Nov 24 '18 at 21:55











      4












      $begingroup$


      • 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.



      :)






      share|cite|improve this answer











      $endgroup$


















        4












        $begingroup$


        • 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.



        :)






        share|cite|improve this answer











        $endgroup$
















          4












          4








          4





          $begingroup$


          • 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.



          :)






          share|cite|improve this answer











          $endgroup$




          • 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.



          :)







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Nov 24 '18 at 22:21

























          answered Nov 24 '18 at 21:59









          Maged SaeedMaged Saeed

          8921417




          8921417























              1












              $begingroup$

              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 $-8$.






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                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 $-8$.






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  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 $-8$.






                  share|cite|improve this answer









                  $endgroup$



                  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 $-8$.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Nov 25 '18 at 3:21









                  SomosSomos

                  15.1k11437




                  15.1k11437






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3012130%2fwhat-number-comes-next-in-this-sequence%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      這個網誌中的熱門文章

                      Xamarin.form Move up view when keyboard appear

                      圖片
                      .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I'm trying to build a Chat app UI, the idea of the Layout was pretty simple: When the input bar is focused, keyboard show up and "push" up the chat bar, as it's a grid, the ListView will resize to fit the screen: I update the input bar's margin to "push" it up: NSValue result = (NSValue)args.Notification.UserInfo.ObjectForKey(new NSString(UIKeyboard.FrameEndUserInfoKey)); CGSize keyboardSize = result.RectangleFValue.Size; if (Element != null){ Element.Margin = new Thickness(0, 0, 0,keyboardSize.Height); //push the entry up to keyboard height when keyboard is activated } And this is ...
                      閱讀完整內容

                      Post-Redirect-Get with Spring WebFlux and Thymeleaf

                      圖片
                      .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 2 Can someone explain to me how to implement the post-redirect-get pattern in Spring WebFlux and Thymeleaf? What subscribes on the database save method? @GetMapping("/register") public String showRegisterForm(Model model) { model.addAttribute("user", new User()); return "register"; } @PostMapping public String processRegisterForm(@Valid User user, BindingResult bindingResult) { if (bindingResult.hasErrors()) { return "register"; } else { userRepository.save(user); //what subscribes on this? //how to redirect on e.g. "/login"? ...
                      閱讀完整內容

                      Anylogic : not able to use stopDelay()

                      圖片
                      -2 I am building a railway station model. I want a train to depart when I click a button. I want to call stopDelay() for that but I am not sure how to do that and from which place. anylogic share | improve this question asked Nov 23 '18 at 10:12 Anupam Singh Anupam Singh 1 Hi Anupam, welcome to SOF. Please check how to ask good questions, see link below. Your question is...
                      閱讀完整內容