My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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
gretchen is offline  
 
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?
roadnottaken is offline  
March 30th, 2007, 09:53 AM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 18,961
Thanks: 1606

In general, a_k = 2^(k + 2) - 3.
skipjack is online now  
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?
Infinity is offline  
April 1st, 2007, 04:34 PM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 18,961
Thanks: 1606

Yes, but I gave the result to cover the cases that roadnottaken (for practical reasons) excluded.
skipjack is online now  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
sequence



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Sequence johnr Number Theory 7 March 17th, 2013 05:02 PM
sum of sequence gelatine1 Algebra 2 March 12th, 2013 11:29 PM
sequence of the average of a sequence elim Real Analysis 8 May 23rd, 2010 12:23 PM
What's next in this sequence? yield Algebra 0 July 26th, 2009 08:05 AM
cauchy sequence that isn't a fast cauchy sequence babyRudin Real Analysis 6 October 10th, 2008 11:11 AM





Copyright © 2018 My Math Forum. All rights reserved.