My Math Forum Sequence #2

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 11th, 2007, 06:51 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, 02:48 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, 09:53 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,718 Thanks: 1806 In general, a_k = 2^(k + 2) - 3.
March 31st, 2007, 05:30 AM   #4
Senior Member

Joined: Dec 2006

Posts: 1,111
Thanks: 0

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, 04:34 PM #5 Global Moderator   Joined: Dec 2006 Posts: 19,718 Thanks: 1806 Yes, but I gave the result to cover the cases that roadnottaken (for practical reasons) excluded.

 Tags sequence

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post johnr Number Theory 7 March 17th, 2013 05:02 PM gelatine1 Algebra 2 March 12th, 2013 11:29 PM elim Real Analysis 8 May 23rd, 2010 12:23 PM yield Algebra 0 July 26th, 2009 08:05 AM babyRudin Real Analysis 6 October 10th, 2008 11:11 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top