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!

Relationship between A.P & G.P

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data

    the Pth, Qth & Rth terms of an arithmetic sequence are in geometric progression. Show that the common ratio is (q-r)/(p-q) or (p-q)/(q-r).

    2. Relevant equations
    for an A.P, the Nth term=
    a (n-1)d
    for a G.P, the Nth term= ar^(n-1)

    3. The attempt at a solution

    let the Pth, Qth & Rth term be
    p, q & r respectively. Since they are in A.P,
    "d"= q-p = r-q
    also, since they form a GP,
    "r"= (p/q)or(q/p)= (r/q)or(q/r)
    don't really know if to make the assumption that for this case, "d"= "r", is pretty safe!
    So please what do i do next?
    Thanks in anticipation!
     
  2. jcsd
  3. Oct 5, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Anyiam! :smile:
    uhh? :confused:

    they'll be a + pd etc :wink:
     
  4. Oct 5, 2012 #3
    Oops! That was some silly mistake on my part! The Pth, Qth & Rth term ought to have been: a plus(p-1)d,
    a plus(q-1)d, and
    a plus(r-1)d respectively!
    pls permit me to use "plus" to indicate addition.
    Going by this, the difference between the
    Qth & Pth term becomes
    d(q-p) and between the
    Rth & Qth term also becomes d(r-q), & equating both gives:
    d(q-p)= d(r-q).
    So what do i do next?
     
  5. Oct 5, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    what are you doing? :confused:

    the question says …
    ie (a + pd)/(a + qd) = (a + qd)/(a + rd)
     
  6. Oct 5, 2012 #5
    Ok! You are right! Because the common ratio must be the ratio between any two consecutive terms say the Pth term[a plus pd] & the Qth term[a plus qd]. But how do i proceed from here?
     
    Last edited: Oct 5, 2012
  7. Oct 5, 2012 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    carefully, but with confidence!

    show us what you get :smile:
     
  8. Oct 5, 2012 #7
    i think the next thing is to eliminate the "d" & "a".
     
    Last edited: Oct 5, 2012
  9. Oct 5, 2012 #8
    Well, i eventually did it this way:
    [Pth term - Qth term] /
    [Qth term - Rth term] and i got (p-q)/(q-r).
    and taking the inverse will also give (q-r)/(p-q), which is true!
    please is this method satisfactory?
     
    Last edited: Oct 5, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook