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Math Help - AP/GP question

  1. #1
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    AP/GP question

    Here goes:

    The first 3 terms of a geometric progression, with first term a = 1 and common ratio r, r does not equal 1, are the 1st, 2nd and 4th term of an arithmetic progression. Find the value of r. (Answer: r = 2)

    I got 3 as my answer though. Thanks in advance if you could help solve this question!
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  2. #2
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    Quote Originally Posted by margaritas
    Here goes:

    The first 3 terms of a geometric progression, with first term a = 1 and common ratio r, r does not equal 1, are the 1st, 2nd and 4th term of an arithmetic progression. Find the value of r. (Answer: r = 2)

    I got 3 as my answer though. Thanks in advance if you could help solve this question!
    For the G.P.,
    a = 1
    common ratio = r  (r is not equal to 1)
    a_2=r
    a_3=r^{2}

    Now since the first three terms of the G.P. are the first, second and fourth terms of an A.P., therefore for the A.P.
    t = 1
    t_2=r
    t_4=r^{2}
    common difference,d=t_2-t=r-1

    Since fourth term of the A.P. is the third term of the G.P.
    a_3=t_4=t+3d
    r^{2}=1+3(r-1)
    r^{2}=1+3r-3
    r^{2}-3r+2=0
    (r-2)(r-1)=0
    r=1,r=2
    But since r is not equal to 1(given), hence \boxed{r=2}.
    I got 3 as my answer though.
    I think you probably made a mistake in factorisation.
    Last edited by shubhadeep; September 2nd 2006 at 09:38 PM.
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  3. #3
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    Oh so the 'a' for AP is assumed to be 1 as well?

    EDIT: Thanks for the solution, shubhadeep!
    Last edited by margaritas; September 2nd 2006 at 10:11 PM.
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  4. #4
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    Quote Originally Posted by margaritas
    Oh so the 'a' for AP is assumed to be 1 as well?
    Its not an assumption. Your question clearly states that.
    Quote Originally Posted by margaritas
    The first 3 terms of a geometric progression, with first term a = 1 and common ratio r, r does not equal 1, are the 1st, 2nd and 4th term of an arithmetic progression.
    The first term of the G.P. is the first term of the A.P., the second term of the G.P. is the second term of the A.P. and the third term of the G.P. is the fourth term of the A.P.
    Last edited by shubhadeep; September 2nd 2006 at 10:49 PM.
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  5. #5
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    Oh ok, silly me.
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