mathematics for business

the third and the sixth term of a G.p are 5 and -40 respectively. find the tenth term of the sequence?

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  1. using the definitions of a GP

    ar^2 = 5
    ar^5 = -40
    divide the second by the first
    r^3 = -8
    r = -2

    back in the first:
    ar^2 = 5 ---> a(4) = 5
    a = 5/4

    term(10) = ar^9
    = (5/4)(-2)^9
    = (5/4)(512)
    = -640

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