Geometric Sequence and Recursive Definition

  • Thread starter rought
  • Start date
  • #1
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Homework Statement



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

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

Homework 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...
 

Answers and Replies

  • #2
34,535
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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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