1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequence problem

  1. Nov 7, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the next three numbers in this sequence... 4, 16, 21, 21, 18, 14, 11, ...

    2. The attempt at a solution
    The difference between each term is 12, 5, 6, 0, -3, -4, -3 but I can't see a pattern and I am completely stuck... Any help pls?
     
  2. jcsd
  3. Nov 7, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    It follows a third-order polynomial, but that would be a weird solution.
    Those questions are always problematic, because you can find rules for arbitrary sequences. Even for a sequence that starts like yours and then goes to 1000 for the next three numbers.

    Could there be a typo somewhere?
     
  4. Nov 7, 2014 #3
    I have doubled and tripled checked... it is indeed , 16, 21, 21, 18, 14, 11, ... and the question is find the next three terms in the given sequence.
     
  5. Nov 7, 2014 #4
    sorry 4, 16, 21, 21, 18, 14, 11, ...

    It is unusable for me...
     
  6. Nov 7, 2014 #5

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What is the context?
    i.e. is it a homework assignment or something as part of some coursework?
     
  7. Nov 7, 2014 #6
    It is a past paper exam question at my school...
     
  8. Nov 7, 2014 #7
    I think the answer is 5,-6,-24
     
  9. Nov 7, 2014 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I get 11, 16, 28.
     
  10. Nov 7, 2014 #9

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I agree with Ray. And for good measure the next term after his is 59.
    [Edit:] Arithmetic mistake: 49. Thanks mfb.
     
    Last edited: Nov 7, 2014
  11. Nov 7, 2014 #10
    Ray is correct I revised the way I did the math and I see where I went sour. The following 3 numbers are: 11, 16, 28. I apologize for misleading people and posting the wrong answer. I did it by first finding the differences of the original numbers in the sequence. (12,5,0,-3,-4,-3.) Next you find the difference of the numbers that are the difference of the sequence. Finally you find the pattern in -7,-5,-3,-1,1,3,5 (the difference of the numbers that are the difference of the numbers in the sequence.) It sounds more complicated than it is.
     
  12. Nov 7, 2014 #11

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I think you mean 49.
    Well, the number of parameters is lower than the number of sequence elements we have, but still... that rule is quite complicated. And there is always a rule like that, if you calculate the differences long enough.
     
  13. Nov 7, 2014 #12

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ... OK, the trick is to relate the question to the kids of problems you've done in school.
    If the past exam paper is more than a couple of years past, though, it may be that the type of sequence they want you to think up has changed since then.

    You have already eliminated the constant-difference type... any others you've seen examples of?
    Look over class exercises or homework.

    To a certain extent, this sort of problem is like "guess the number I just thought of"... so you need a way to narrow down what is possible.
    Note: when you plot ##x_n## vs ##n## it does kinda look like it's trying to be a cubic or some fancy exponential. If you have seen sequences like ##x_n=P_m(n)## (Where ##P_n(x)## is a polynomial in x of order n) then that is one way to go.

    You could also attempt to decipher the clues in Ray and LC's posts.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Sequence problem
  1. Sequence problem (Replies: 4)

  2. Problem with a sequence (Replies: 34)

  3. Sequences problem (Replies: 6)

  4. Sequence Problem (Replies: 1)

  5. Sequence problem (Replies: 10)

Loading...