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Can you help me solve these sequences

  1. Jan 17, 2008 #1
    Dear all,

    I would highly appreciate if you could help me solving the following sequences:

    Question 1: 3,5,8,24,209,3591,?

    Question 2: 4,7,13,21,34,55,88,?

    Question 3: 8,12,18,27,42,70,126,241,?

    Question 4: 3,8,23,60,137,256,?

    Question 5: 5,10,19,32,49,70,?
  2. jcsd
  3. Jan 17, 2008 #2


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    Staff: Mentor

    Have you tried to find the pattern for each of these problems? Try Question 5, you should recognize the pattern by the time you get to 19.

    Finding the pattern is the fun in doing these types of problems.

    May I ask what those numbers listed under the question are? The question is asking what comes after 70, but none of the numbers below are correct following the pattern.
    Last edited: Jan 17, 2008
  4. Jan 17, 2008 #3
    Of course, 95 is the correct answer!
  5. Jan 17, 2008 #4


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    Staff: Mentor

    Duh, I missed the 95. Completely skipped over it.

    And you gave away the answer!
  6. Jan 17, 2008 #5
    Thanks! I figured it out why 95 is the answer for question 5:

    10 - 5 = 5
    19-10 = 9
    32-19= 13
    49 - 32 = 17
    70 - 49 = 21

    Consider the sequence : 5, 9, 13, 17, 21 the increment is 4. Thus, the next number is something that is greater than 70 by 21+4=25.

    How about questions 1 - 4? Can anyone find the solution?

    Have A Great Day!
  7. Jan 22, 2008 #6
    I have solved the third question. The others are not easy. If anybody wants a hint, just ask :-)

    @ wonderful: Is there a change that you have gotten these questions from the following site? http://www.allthetests.com/quiz18/quizpu.php?testid=1141425609 If so then you have forgotten a possible solution at question 2, namely 140. Whether this is the right solution or not I can't tell because I haven't been able to solve this one so far.

    There are also 5 other questions, 6 to 10 of which I have solved 9 and 10. If wanted you might post them, I'm not going to because I don't want to mess up your post.

    Anybody else solved one of the others?
  8. Jan 24, 2008 #7
    I had been out of town in the last two days. Coomast is correct in saying that 140 is also one of the choices in question 2. Coomast can you give us a hint for question 3? These questions are very interesting.

    Have A Great Day!
  9. Jan 24, 2008 #8
    A hint for question 3: use the same principle as for solving question 5. Write line per line the differences of two adjacent numbers. Can you see a known sequence after 4 lines of differences? Hope this is clear, otherwise please ask.

    I'm working on question 1 and I think I've got something. I'm now working on the general formula, but it isn't straightforward.

    These are very strange as a IQ test. One can't possibly have the time to solve all of them within the time frame of such a test. On the other hand they are very nice brain teasers indeed :-)
  10. Jan 24, 2008 #9
    Thanks coomast for the hint. As you suggested, I looked at the sequence of difference between two adjacent numbers: 4, 6, 9, 15 .... but saw no clear pattern. Can you help? It seems to mention on the related website that there is no time limit on these kind of questions.
  11. Jan 25, 2008 #10
    Take the differences again for this newly created line, and again, and again. Then you can see a pattern related to some powers.

    I've solved the first one as well, this is an even more complicated sequence. A hint: take the differences as done before a few times. Then a pattern involving 13 appears together with the adding of another sequence. This is a complicated one indeed. The general formula looks awesome.

    The general formula for question 5 can be written as:

    [tex]x_n=4+2 \cdot x_{n-1}-x_{n-2}[/tex]

    It is a nice exercise to look for these as well.
  12. Jan 25, 2008 #11
    Cool! Thanks coomast. I found the answer for question 3 is 478. I am going to solve question 1. These questions are very interesting and great for brain.
  13. Jan 25, 2008 #12
    Thanks to coomast hint, I've found the solution for question 1: 35534. Thus, we have two not-yet-solved questions 2, 4. After solving these two, I will post new questions that are as intersting as the above 5.
  14. Jan 25, 2008 #13
    Indeed wonderful, that's the one. I will try to look for the second and fourth sequence.
  15. Jan 25, 2008 #14
    Following the same line of logic, I found the solution for question 2 is 140

    Have A Great Day!
  16. Jan 26, 2008 #15
    Can you give an additional hint on sequence 2? I don't see a pattern.

    [Edit] Is it possible that the next number after 140 equal is to 219?
    Last edited: Jan 26, 2008
  17. Jan 26, 2008 #16
    I am very happy to share ideas with you. Take the first difference we have: 3, 6, 8, 13, 21, 33. Take the second difference we have 3, 2, 5, 7, ... Here, we can see: 3+2=5, 2+5=7, and so on...

    Please feel free to let me know if this helps.
    Have A Great Day!
  18. Jan 27, 2008 #17
    Hello wonderfull, I looked at this for some time and didn't see any order in it. Finally I figured it out, I think you made an error. The sequence of the differences of the differences reads: 3 2 5 8 12, you seem to have a 7 instead of the 8. Or am I missing something?
  19. Jan 27, 2008 #18
    Hi coomast
    Thanks for pointing that out. Could you give us a hint on this question.
    Have A Great Day!
  20. Jan 29, 2008 #19
    I didn't solve this one yet, also number 4 seems almost a random number writing. I keep working on it.
  21. Feb 3, 2008 #20
    Sorry wonderful, I can't find the others. :confused: :frown: :cry:
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