1. Not finding help here? Sign up for a free 30min 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!

In terms of n, 3, 7, 13, 27, 53, 107

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the explicit formula c1=1, c2=2, cn+1 = (cn + cn-1)/2 ; n>2


    2. Relevant equations



    3. The attempt at a solution

    c1 = 1
    c2 = 2
    c3 = 3/2
    c4 = 7/4
    c5 = 13/8
    c6 = 27/16
    c7 = 53/32
    c8 = 107/64

    I know the bottom term is 2^n-2. I cannot find what the top is. If anyone sees it let me know thx.

    Also if you know general form of 1, 1, -1, -1, 1, 1, -1, -1 ....

    Thx a lot
     
  2. jcsd
  3. May 12, 2010 #2
    The numerator kind of looks like [tex]a_{n+2}=2a_{n}+a_{n+1}[/tex] to me, so it would be like this:
    c4 = (2*2) + 3 = 7
    c5 = (2*3) + 7 = 13
    c6 = (2*7) + 13 = 27
    etc, it only works when n > 2 which seems to fit into what you mentioned as well. Hope that helps a bit!
     
  4. May 12, 2010 #3

    lanedance

    User Avatar
    Homework Helper

    try multplying out explicitly for the first few terms - you should hopefully be able to pick up a pattern in terms of sums of powers of 2
    [tex]3 = 1+2[/tex]
    [tex]7 = 1 +2+2^2[/tex]
    and follow on from there...
     
  5. May 12, 2010 #4
    I was told you cannot use the terms before it in the equation, ie. cn-1*2 + (-1)^n
     
  6. May 12, 2010 #5

    lanedance

    User Avatar
    Homework Helper

    i'm not sure i know what you mean? try this though, write the c_n in term of a new variable a_n, for n>2
    [tex]c_1 = 1[\tex]
    [tex]c_2 = 2[\tex]
    [tex]c_3 = \frac{3}{2} = \frac{a_3}{2}[\tex]
    [tex]c_4 = \frac{7}{2^2} = \frac{a_4}{2^2}[\tex]

    so you want to find the a_n, with
    [tex]c_n = \frac{a_n}{2^{n-2}}[\tex]

    how about seeing if you can find a recursion relation for the a_n, using the original... will be similar to what refraction posted, but the form should help lead to a general solution.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: In terms of n, 3, 7, 13, 27, 53, 107
  1. N term metrix question (Replies: 7)

Loading...