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Homework Help: Arithmetic sequence, geometric sequence

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Posted this thread earlier but had mis read the given answer. please disregard older thread as I dont know how to delete it!

    Write down the condition for the numbers p, q, r to form an arithmetic sequence & geometric progression.

    2. Relevant equations

    \ a_n = a_1 + (n - 1)d, ???

    3. The attempt at a solution
    Have no idea, tried looking for similar examples on the net but they all seem to include numbers that are euidistant ie 5, 7, 9, 11......

    All help is appreciated if someone could point me in the right direction about how to go about this!!
  2. jcsd
  3. Feb 25, 2012 #2


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    hi sg001! :wink:
    well, isn't that the answer, then? :smile:
  4. Feb 25, 2012 #3
    so just to make sure i understand whats goin on here.../

    If i had the same question but now with a,b,c,d,e,f.

    The conditions for arithmetic sequence containing these numbers would be...

    a = 1/5(b+c+d+e+f)
  5. Feb 25, 2012 #4


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    i] nooo

    ii] just do it for p q and r …

    what is the equation that p q and r (only) have to satisfy?

    (in other words: translate what you've already said into an equation :wink:)
  6. Feb 25, 2012 #5
    ok so it is

    p= 1/2 (q +r)

    but is this the case for questions with a larger amount of terms

    ie p,q,r,s,t,u

    where i can say to satisfy an arithmetic sequence

    p= 1/5 (q +r+ s+t+u)

    because this is how im understanding whats goin on

    ie 2p = q +r

    & 5p = q + r +s +t +u
  7. Feb 25, 2012 #6
    Or does it only work because q is the middle term
    Therefore p & r are equidistant from q .
    Hence, q = 1/2 (p + r)

    So it will only work with an odd amount of numbers ie a,b,c or a,b,c,d,e
    By working it out simply that is??
  8. Feb 25, 2012 #7


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    hi sg001! :smile:
    you mean q = 1/2 (p +r) :wink:
    no, you need an extra equation for each extra term

    (eg 5 terms, 3 equations)
  9. Feb 25, 2012 #8
    Okie I understand now.
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