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Find the nth term of the sequence (Explicit formula)

  1. Jul 21, 2015 #1
    1. The problem statement, all variables and given/known data
    { 7/6 , 45/54 , 275/648, 1625/9720 ... }

    Problem from a practice exam. My instructions are to find an explicit formula for the above sequence..

    3. The attempt at a solution

    Let An =7/6 , 45/54 , 275/648, 1625/9720 ...

    Allow An = Bn / Cn

    Bn = 7, 45, 275, 1625.... (2n+5) 5n-1 starting at n = 1

    Cn = 6,54,648,9720.... 3(n+1) [ What multiplies here is the preceding term, so if we allow n = 2 , we multiply the expression by 6 to get 54, if we allow n = 3, we multiply by 54 to get 648, if we allow n = 4, we multiply by 648 to get 9720.

    I have no idea how to express this, or if there is a better way.
     
    Last edited: Jul 21, 2015
  2. jcsd
  3. Jul 21, 2015 #2
    Cn=Cn-13(n+1) and declare that C0=1
     
  4. Jul 21, 2015 #3
    ∴ Starting at n=1 An = (2n+5) 5n-1 / 3(n+1) Cn-1 , where we have declared C0 = 1

    Noting that Bn & Cn equal what we have defined above.

    Correct?
     
  5. Jul 21, 2015 #4
    The entire sequence can't be indexed by two letters, A and C, you need to find a form where you only need A
     
  6. Jul 21, 2015 #5
    So I have to rewrite Cn in terms of A only? Is this possible? I am drawing a complete blank :))
     
  7. Jul 22, 2015 #6
    Figured it out!
     
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