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    AEltusya's Avatar
    AEltusya Posts: 2, Reputation: 1
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    #1

    Dec 11, 2013, 01:25 AM
    Geometric
    The sum of three successive terms of a geometric sequence is 35/2 while their product is 125. Find the three terms
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 11, 2013, 07:23 AM
    Given A = the first term and r is the ratio of successive terms, the brute force way to solve this is to set up two equations in two unknowns of A and r:

    A + Ar + Ar^2 = 35/2
    A(Ar)(Ar^2) = A^3r^3 = 125

    This is a bear to solve. So here's a hint: note that 125 = 5^3, hence the product of Ar = 5. Try different values of A and r whose product is 5 ,and see what works.
    AEltusya's Avatar
    AEltusya Posts: 2, Reputation: 1
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    #3

    Dec 12, 2013, 06:41 AM
    Quote Originally Posted by ebaines View Post
    Given A = the first term and r is the ratio of successive terms, the brute force way to solve this is to set up two equations in two unknowns of A and r:

    A + Ar + Ar^2 = 35/2
    A(Ar)(Ar^2) = A^3r^3 = 125

    This is a bear to solve. So here's a hint: note that 125 = 5^3, hence the product of Ar = 5. Try different values of A and r whose product is 5 ,and see what works.
    Awesome! Thanks :)
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