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:
 
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.


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