My Math Forum Sequence #2

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 11th, 2007, 07:51 PM #1 Newbie   Joined: Jan 2007 Posts: 18 Thanks: 0 Sequence #2 One more sequence problem I have having problems with: Find the third term in the recursively defined sequence: a[sub 1]=5, a[sub k+1]=2[sub ak]+3. Possible answers: 9 11 13 29
 February 12th, 2007, 03:48 AM #2 Senior Member   Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 When the term to find is not excessively large (e.g. a_50), the simplest way to find it is by using the recursive definition to find each term up to and including the term you are supposed to find. a_1 = 5 a_2 = 2(a_1) + 3 = 13 a_3 = 2(a_2) + 3 = 29 Just to make certain, the recursive definition was a_1 = 5, a_(k+1) = 2*a_k + 3, correct?
 March 30th, 2007, 10:53 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 In general, a_k = 2^(k + 2) - 3.
March 31st, 2007, 06:30 AM   #4
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Quote:
 In general, a_k = 2^(k + 2) - 3.
Is that basically changing the recursive definition to an equivalent non-recursive definition?

 April 1st, 2007, 05:34 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 Yes, but I gave the result to cover the cases that roadnottaken (for practical reasons) excluded.

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