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!

Formula and Sequence

  1. Apr 10, 2010 #1
    I just wanted to know if anybody had a trick to find the formula for the general term of a sequence.

    I can find some without troubles. But other like 1,0,1,0,1,0... I don't know how to find them.

    Thank you!
     
  2. jcsd
  3. Apr 10, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Of course you know that technically, the next term could be anything and the first few terms of a sequence never determines a pattern. So these questions always involve a subjective judgement or guess what the author intends. In this case one suspects the described sequence is to consist of alternating 1's and 0's. It is more a matter of experience than anything to come up with a formula. This might suggest sin(n pi/2) for n = 1,2,..., which gives:

    1 0 -1 0 1...

    Not quite it. Put absolute values on it: |sin (n pi/2)|:

    1 0 1 0 ... works.

    Another thing you might think of is using (-1)n, which alternates the sign:

    -1 1 -1 1 -1 1...

    Try adding 1 to it: 1 + (-1)n: 0 2 0 2 0 2...

    Close. Divide it by 2: (1 + (-1)n)/2: 0 2 0 2 0 2 if you start with n = 1. So start with n = 0.

    Each problem presents its own challenges.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Formula and Sequence
  1. Formulas for sequences (Replies: 3)

Loading...