Results 1 to 3 of 3

Math Help - Another arithmetic sequence problem

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    68

    Another arithmetic sequence problem

    For a given arithmetic sequence, u_n=m and u_m=n. Find

    a) the common difference.
    b) u_n+m.


    Answers: a) -1, b) 0

    Could someone explain to me the method?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    56
    I would think that Un + m would equal 2m since Un = m. Could you explain why that is not the case?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,807
    Thanks
    697
    Hello, shawli!

    You typed part (b) incorrectly . . .


    For a given arithmetic sequence: . \begin{array}{ccc}u_n&=&m \\ u_m &=& n \end{array}

    Find: . \text{(a) the common difference }
    . . . . . (b)\;u_{m+n}

    Answers: . (a)\;\;\text{-}1,\quad (b)\;\; 0
    The k^{th} term is given by: . u_k \;=\; a + (k-1)d . where: . \begin{Bmatrix}a &=& \text{first term} \\ d &=& \text{common diff.} \end{Bmatrix}


    We have: . \begin{array}{ccccccccc}u_n \:=\:m & \;\Rightarrow\; & a+(n-1)d \:=\:m & \;\Rightarrow\; & a \:=\:m-(n-1)d & [1] \\ u_m \:=\:n & \Rightarrow & a+(m-1)d \:=\:n & \Rightarrow & a \:=\:n-(m-1)d & [2] \end{array}


    Equate [1] and [2]: . m - (n-1)d \:=\:n-(m-1)d \quad\Rightarrow\quad m-dn \:=\:n - dm

    . . . . . . m - n + dm - dn \:=\:0 \quad\Rightarrow\quad (m-n) + d(m-n) \:=\:0  \quad\Rightarrow\quad (m-n)(d+1) \:=\:0


    If m-n\:=\:0 \quad\Rightarrow\quad m \:=\:n , we have: . u_m \:=\:m
    . . and the arithmetic sequence cannot be determined.

    If d+1 \:=\:0, then: . \boxed{d \:=\:-1}



    u_{m+n} \;\;=\;\;a + (m+n-1)d \;\;=\;\;a + md + nd - d

    . . . . =\;\;a + md - d + nd \;\;=\;\;\underbrace{a + (m-1)d}_{\text{This is }u_m \,=\, n} + nd \;\;=\;\;n + nd


    Since d = \text{-}1, we have: . u_{m+n} \;=\;n + n(\text{-}1) \;=\;0

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  2. Arithmetic Sequence problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 3rd 2010, 01:47 PM
  3. arithmetic sequence problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 2nd 2010, 02:21 PM
  4. arithmetic sequence problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 26th 2009, 07:24 PM
  5. arithmetic sequence problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 25th 2008, 07:53 PM

Search Tags


/mathhelpforum @mathhelpforum