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Math Help - Progression problems........

  1. #1
    Junior Member
    Joined
    Jul 2010
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    Progression problems........

    The following two problems are baffling me to no end..... please help!

    1) In a Geometrical Progression , prove that the product of any two terms, equidistant from the beginning and the end, is constant and is equal to the product of the first and last terms.

    2) Prove that the product of the two middle terms of a Geometrical Progression, consisting of an even number of terms is equal to the product of the first and last terms.
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  2. #2
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
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    Post

    answer to 1:-

    let the progression is given by  a, ar, ar^2, ar^3, ....... , ar^{n-1} where  r is the common ratio and  a is the first term and the progression possesses  n terms.
    let us take  kth term from the beginning and end, respectively. the terms are then given by  ar^{k-1} and  ar^{n-k+1-1} (ie,  n-k+1th term from the beginning). so their product is given by  a^2r^{k-1+n-k+1-1} ie  a^2r^{n-1} .
    also, the product of the first and last terms of the progression is  a*ar^{n-1} = a^2r^{n-1} .

    hence the result.

    try the second one yourself. best of luck.
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