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  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
 
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.


Tags 
sequence 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sequence  johnr  Number Theory  7  March 17th, 2013 06:02 PM 
sum of sequence  gelatine1  Algebra  2  March 13th, 2013 12:29 AM 
sequence of the average of a sequence  elim  Real Analysis  8  May 23rd, 2010 01:23 PM 
What's next in this sequence?  yield  Algebra  0  July 26th, 2009 09:05 AM 
cauchy sequence that isn't a fast cauchy sequence  babyRudin  Real Analysis  6  October 10th, 2008 12:11 PM 