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Math Help - Sequence and Series

  1. #1
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    Question Sequence and Series

    I'm having problems getting started on this question. I think once this parts cracked I can continue with the other parts.

    The 1st, 2nd & 3rd terms of an AP are p , q & p^2 resepctively, where p is negative.

    The 1st, 2nd & 3rd terms of a GP are p , p^2 & q resectively.

    Show that p = -1/2 and find the value of q.

    So, as this is an AP I know that U_2 - U_1 = U_3 - U_2 = d

    Therefore, (q - (-p)) = (p^2 - q)
    rearrange and I get q = (p^2 - p)/2 = d

    I try subbing this in for U_2: a + 2d = q
    as I have just found q and d to be (p^2 - p)/2

    I dont end up with -1/2 though. Am I approaching this completely wrong or have I made a schoolboy error.

    Your help is much appreciated - I have a test tomorrow!!!

    thanks, D
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  2. #2
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    Knowing that p is negative, there's no need to write it as such. That is...

    From the AP: q - p = p^2 - q

    From the GP: p^2/p = q/p^2

    Solve the simultaneous equations, finding two values for p, only one of which is correct with the given condition. Then use either one of the equations to find q.
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  3. #3
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    Question

    Great! So I use substitution to solve the simultaneous eq. and get

    p (-2p^2 + p + 1) = 0

    when p = 0 , p = 1 , p = -1/2

    p cannot equal 0 as it would be convergent, p cannot equal 1 because the GP would not be defined and therefore it must be p = -1/2

    is this right??

    D
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  4. #4
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    I've looked at this again and I see that p must be -1/2 because this is defined in the question - It is negative!

    I get 3/8 for q
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