Results 1 to 6 of 6

Math Help - Find Closed Form given Recursive Formula

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    32

    Find Closed Form given Recursive Formula

    Recursive formula:

    a_n=5*a_{n-1} with a_1 = 5

    Can someone please show me how to do this? I'm studying for a test and need to see the step in order to proceed with the rest of these types of problems.

    The question asks to find the next 5 terms of the sequence and then provide the Closed Form.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by Edbaseball17 View Post
    Recursive formula:
    a_n=5*a_{n-1} with a_1 = 5
    Surely you see that a_n = 5^n?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    32
    Here is what I've tried and it is not working.

     a_1=5(0)
    a_2=5(1)

    and so on.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,408
    Look at your recursion again: a_n = 5a_{n-1}

    So, we have:
    \begin{aligned} a_1 & = 5 \\ a_2 & = 5a_1  = 5 \times 5 = 5^2 \\ a_3 & = 5a_2  = 5(5^2) = 5^3 \\ a_4 & = 5a_3 = 5(5^3) = 5^4 \\ & \qquad \qquad  \vdots \\ a_n & = \cdots \end{aligned}

    See how Plato's suggestion comes into play?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by Edbaseball17 View Post
    Here is what I've tried and it is not working.
     a_1=5(0) a_2=5(1)
    No indeed!
    You were given that a_1=5 then a_{\color{blue}1}=5^{\color{blue}1}.
    Also we know that a_n = 5 a_{n-1} so a_2=5(a_1)=5(5)=5^2.
    Do you understand?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Aug 2007
    Posts
    32
    I'm an idiot. Yea i got it now. I was substituting the sub numbers instead of using the finished product of the equation. Thanks Plato!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 25th 2010, 05:11 AM
  2. Recursive formula find closed something
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 28th 2010, 02:32 AM
  3. Find a closed form
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 28th 2009, 06:31 AM
  4. Converting Closed Form to Recursive Formula
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 20th 2009, 02:38 PM
  5. Find the closed-form of the series.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 20th 2008, 09:37 AM

Search Tags


/mathhelpforum @mathhelpforum