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If told that the 3rd term of a GP is 36 and the 8th term is 8748. find the first term and the common ration.

  • maths -

    start with 4 with a factor of 3

    4 12 36 for the 3rd

  • maths -

    The n - th term of a geometric progression with initial value a and common ratio r is given by:

    an = a * r ^ ( n - 1 )

    In this case :

    a3 = a * r ^ ( 3 - 1 ) = a * r ^ 2 = 36

    a8 = a * r ^ ( 8 - 1 ) = a * r ^ 7 = 8748

    So you must solve two equations :

    a * r ^ 2 = 36

    and

    a * r ^ 7 = 8748


    a * r ^ 2 = 36 Divide both sides by r ^ 2

    a * r ^ 2 / r ^ 2 = 36 / r ^ 2

    a = 36 / r ^ 2


    a * r ^ 7 = 8748 Divide both sides by r ^ 7

    a * r ^ 7 / r ^ 7 = 8748 / r ^ 7

    a = 8748 / r ^ 7


    a = a

    36 / r ^ 2 = 8748 / r ^ 7 Multiply both sides by r ^ 7

    36 * r ^ 7 / r ^ 2 = 8748 * r ^ 7 / r ^ 7

    36 * r ^ 5 = 8748 Divide both sides by 36

    36 * r ^ 5 / 36 = 8748 / 36

    r ^ 5 = 243

    r = fifth root ( 243 )

    r = 3


    a = 36 / r ^ 2

    a = 36 / 3 ^ 2 = 36 / 9 = 4

    OR

    a = 8748 / r ^ 7

    a = 8748 / 3 ^ 7 = 8748 / 2187 = 4



    The first term of a GP:

    a = 4

    The common ratio:

    r = 3

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