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Geometric Sequence and Recursive Definition

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data

    In a Geometric Sequence find t10. t3 = 4 and t6= 4/27

    Give a recursive definition for the sequence: 1, 4, 13, 40....

    2. Relevant equations

    I know that a Geometric sequence is: tn=t1(r)n-1

    And that a recursive formula starts off with tn-1

    I'm not sure where to go from here...
     
  2. jcsd
  3. May 13, 2009 #2

    Mark44

    Staff: Mentor

    A geometric sequence has terms that look like this: {a, ar, ar2, ar3, ...}, where each term is r time the previous term. In your first problem, you have t3 = 4, so t4 = rt3 = 4r, t5 = 4t4 = ? Just work your way up to the ones you want to find.

    In your second problem, you have {1, 4, 13, 40, ...}
    The 2nd term is the first plus 3. The 3rd term is 9 plus the 2nd. The 4th term is 27 + the 3rd. Do you see a pattern?
     
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