1. Limited time only! Sign up for a free 30min personal 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 Sequence

  1. Jan 9, 2004 #1
    The first four terms in an arithmetic sequence are x+y, x-y, xy, x/y, in that order. What is the fifth term?
    Can anyone show me how to do it?
    O btw, the fifth term is a number, is not a variable
    Thx
     
    Last edited: Jan 9, 2004
  2. jcsd
  3. Jan 9, 2004 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, you know the first term: x + y.

    You know the second term: x - y.

    So, you can find the difference between successive terms.

    Thus, you can write down the third and fourth terms in a different way, and you'll have two equations in two unknowns.
     
  4. Jan 9, 2004 #3
    No, it would be 3 variable, becuz of the common difference between them, and the system is very complicated, cuz is in terms of x and y
     
  5. Jan 9, 2004 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, but you can solve for the difference in terms of x and y, so there are only two unknowns!


    And it won't be too complicated; have a little faith and try it. :smile: If you get stuck, post how far you got and I can nudge you the rest of the way.
     
  6. Mar 12, 2009 #5
    Let us substitute x = py. Then,((p+1)y, (p-1)y, p*y^2 and p (in this order) are first four terms in an arithmetic sequence with a common difference (c.d) of -2y.

    Thus, (p-3)y = p*y^2 …(i), and:
    (p-5)y = p …(ii)

    From (i), we note that y must be nonzero, otherwise x/y becomes indeterminate. Therefore, (i) forces y = (p-3)/p, while from (ii), we obtain: y = p/(p-5)

    Hence, (p-3)/p = p/(p-5), whereupon in terms of cross multiplication, we obtain:

    p^2 = p^2 – 8p+ 15, so that: p = 15/8, giving: y = -15/25 = -3/5, and:
    x = (15/8)*(-3/5) = -9/8

    So, the c.d = -2y = 6/5, and accordingly:

    The required fifth term = p – 2y = 15/8 + 6/5 = 123/40
     
    Last edited: Mar 12, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Arithmetic Sequence
  1. Arithmetic Sequence (Replies: 4)

  2. Modular arithmetic (Replies: 7)

Loading...