1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arithmetic progression(alternate method)

  1. Sep 6, 2004 #1
    in an arithmetic sequence there is an even number of term's
    the sum of terms in the odd places is 440 and the sum of terms in the even places is 520, the last term is bigger than the first term by 156
    find how many term's the arithmetic sequence has.

    This was from a previous post, but i wanted to figure it out this way.

    I tried out this problem, but i can't seem to go ne where with it.

    For sum of even numbers

    (a+d+a+2d(n-1))*n = 1040<------------ 2an + 2dn^2 -dn = 1040

    For sum of odd numbers

    (a + a +2d(n-1))*n = 880<-------------- 2an + 2dn^2 - 2dn = 880

    solved the two system of equation

    dn = 160

    N = total number = 2n

    Nd = 320

    d(N-1) = 156<----------- d = 164

    so solve for N using Nd = 320 = 320/164 = 1.95.....

    Obviously this is not correct. What did i do wrong here?
  2. jcsd
  3. Sep 6, 2004 #2
    For the even sequence, you should get this


    Solve the 2 equations, get nd=80;Nd=160; Nd-d=156; d=4; N=40.
  4. Sep 6, 2004 #3
    thanks alot, so that's where i went wrong.
  5. Sep 6, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper

    Here's how I did it:

    If you multiply the number of terms in an arithmetic series by the average of the first and last terms the product is the sum of the series. Therefore, the sum of the even terms is

    [tex]\frac {N}{2} \frac {a_2+a_N}{2} = 520[/tex]

    and the sum of the odd terms is

    [tex]\frac {N}{2} \frac {a_1+a_{N-1}}{2} = 440[/tex]

    (Note the sum of the odd terms is even so the [itex]\frac {N}{2}[/itex] is a whole number)

    Now, [itex]a_2 = a_1+d[/itex] and [itex]a_{N-1} = a_N-d[/itex] where d is the common difference. Substitute these into the equations and subtract the two equations to obtain [itex]N d = 160[/itex]
    We also know [itex](N-1)d = 156[/itex] so, dividing gives

    [tex]\frac {N}{N-1} = \frac{160}{156} = \frac {40}{39}[/tex]

    from which N = 40 follows.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Arithmetic progression(alternate method)
  1. Progressive wave (Replies: 1)