June 1st, 2008, 03:12 PM  #1 
Newbie Joined: Jun 2008 Posts: 3 Thanks: 0  "Recursive definition"
Can anyone give "recursive" definition of the sequences given below? n = 1,2,3... Code: a) a_n = 4n2 b) a_n = 1 + (1)^n c) a_n = n(n+1) d) a_n = n^2 Please provide me with explanation too! Also, is there any LaTeX in this forum? 
June 1st, 2008, 04:40 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
If you write out a_n  a_(n1), you'll find the recursive forms fairly easily. For the first, a_n  a_(n1) = (4n  2)  (4(n1)  2) = 4, so a_n = a_(n1) + 4. LaTeX is coming soon! 
June 1st, 2008, 05:15 PM  #3  
Newbie Joined: Jun 2008 Posts: 3 Thanks: 0  Quote:
Code: Is this true for 2nd one... a_n  a_n1 = 2 (1)^n Is this recursive definition correct? for question b)  
June 1st, 2008, 09:43 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
No. (1)^n  (1)^(n1) is either 2 or 2. a_n + a_(n1) = 0.


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give a recursive definition of the sequence {formula173.mml}, n = 1, 2, 3,... if,give a recursive definition of the sequence {an},n=1,2,3,... if a n=n(n 1),a) formula177.mml = 4n – 2 give a recursive definition of the sequence {formula173.mml}, n = 1, 2, 3,... if
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