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 June 1st, 2008, 04:12 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 = 4n-2 b) a_n = 1 + (-1)^n c) a_n = n(n+1) d) a_n = n^2 Thanks for any quick help! Please provide me with explanation too! Also, is there any LaTeX in this forum?
 June 1st, 2008, 05:40 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_(n-1), you'll find the recursive forms fairly easily. For the first, a_n - a_(n-1) = (4n - 2) - (4(n-1) - 2) = 4, so a_n = a_(n-1) + 4. LaTeX is coming soon!
June 1st, 2008, 06:15 PM   #3
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 Originally Posted by CRGreathouse If you write out a_n - a_(n-1), you'll find the recursive forms fairly easily. For the first, a_n - a_(n-1) = (4n - 2) - (4(n-1) - 2) = 4, so a_n = a_(n-1) + 4. LaTeX is coming soon!
Code:
Is this true for 2nd one...

a_n - a_n-1 = 2 (-1)^n

Is this recursive definition correct? for question b)

 June 1st, 2008, 10:43 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)^(n-1) is either 2 or -2. a_n + a_(n-1) = 0.

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

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