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10 October, 21:06

Find the 6th term of a geometric sequence with t1 = 7 and t9 = 45,927.

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  1. 10 October, 21:15
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    GS = a rⁿ ⁻ ¹

    t₁ = 7, a = 7

    t₉ = 45927 ar⁹ ⁻ ¹ = ar⁸ = 45927

    a = 7 ... (a)

    ar⁸ = 45927 ... (b)

    Equation (b) : (a)

    ar⁸/a = 45927/7

    r⁸ = 6561

    Take the eight root of both sides

    ⁸√r⁸ = ⁸√6561

    r = 3

    Sixth term = ar⁶ ⁻ ¹ = ar ⁵ = 7*3⁵ = 1701

    Sixth term = 1701
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