Results 1 to 4 of 4

Math Help - arithmetic sequences: why finding the nth term works

  1. #1
    Junior Member
    Joined
    Oct 2008
    From
    Maine
    Posts
    70

    arithmetic sequences: why finding the nth term works

    I understand HOW to create a formula to find the Nth term in an arithmetic sequence. My question is WHY does it work.

    I understand what the explicit formula represents and how to use it. I am just lost on why all of it works. Why can I multiply the common difference by the nth term, and then add it to the the the first term number minus the common difference and get this magical formula?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    Let a_1,a_2,a_3,... be arithmetic with common difference d.

    Then

    a_2=a_1+d
    a_3=a_2+d=a_1+d+d=a_1+2d
    a_4=a_3+d=a_1+2d+d=a_1+3d

    So, in general

    a_n=a_1+(n-1)d.

    You can prove this formally by mathematical induction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67
    Short 'n sweet (d = common diff, a = 1st term):

    0,3,6,9,12,15... : nth term = d(n-1)

    2,5,8,11,14,17... : comparing to above, each term is higher by a

    Sooooo: nth term = d(n-1) + a ; 3(6-1) + 2 = 17
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2008
    From
    Maine
    Posts
    70
    Thank you drsteve
    That makes much more sense to me now. I had one of my 7th graders ask me why today and I told them I'd figure it out tonight. Really appreciate it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a function that works
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 25th 2010, 07:07 PM
  2. Replies: 4
    Last Post: March 28th 2009, 12:05 PM
  3. Arithmetic sum to nth term
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 14th 2008, 08:21 PM
  4. Sequences - nth Term
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 10th 2007, 06:36 AM
  5. Sequences, find the term
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 27th 2007, 11:37 AM

Search Tags


/mathhelpforum @mathhelpforum