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 problem

  1. Jan 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Let [itex]a_{m+n}=A[/itex] and [itex]a_{m-n}=B[/itex] be members of arithmetic progression then [itex]a_{m}[/itex] and [itex]a_{n}[/itex] are? (m>n).


    3. The attempt at a solution
    I fugured that [itex]a_{m}=\frac{A+B}{2}[/itex] but i have no idea what [itex]a_{n}[/itex] is.
    In my text book solution is [itex]a_{n}=\frac{(2n-m)A + mB}{2}[/itex]
    How did they arrived to that solution?
     
  2. jcsd
  3. Jan 3, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Government$! :smile:
    an = am + (n-m)∆ :wink:
     
  4. Jan 3, 2013 #3
    Hi,

    using the fact that [itex]A-B=2dn[/itex] and plugging that into your equation and then finding
    [itex]a_{n-m}[/itex] from [itex]a_{n}=\frac{A+a_{n-m}}{2}[/itex] i got solution [itex]a_{n}=\frac{(2n-m)A + mB}{2n}[/itex]. So i have one extra [itex]n[/itex] that i cant get rid of.
     
  5. Jan 3, 2013 #4

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    How did you calculate that?
     
  6. Jan 4, 2013 #5

    Curious3141

    User Avatar
    Homework Helper

    I get the same answer you do. I think the textbook has a typo.
     
  7. Jan 4, 2013 #6

    Curious3141

    User Avatar
    Homework Helper

    Because there are 2n terms between term (m-n) and term (m+n), which gives a difference of 2nd, where d is the common difference of the arithmetic progression. So A - B = 2nd.
     
    Last edited: Jan 4, 2013
  8. Jan 4, 2013 #7

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    I am beginning to understand. The difference would need to be even, since there are TWO differences involved among the m and the n terms.
     
  9. Jan 4, 2013 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    [itex]\displaystyle a_{n}=\frac{(2n-m)A + mB}{2n}\ \ [/itex] looks right to me.

    Try some examples to verify it.
     
  10. Jan 4, 2013 #9

    Curious3141

    User Avatar
    Homework Helper

    Sorry, I just noticed a typo in my post (since edited and corrected). I meant that since there are 2n terms between the two terms, the difference is 2nd.

    There is only one common difference d in an arithmetic progression.
     
  11. Jan 4, 2013 #10
    Thanks for help, everybody.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Arithmetic progression problem
Loading...