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22 January, 19:35

The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3

What is the first term of the series?

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  1. 22 January, 19:51
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    81

    Step-by-step explanation:

    The formula for calculating the sum of geometric series varies depending on the value of its common ratio.

    Given the common ratio to be 2/3 which is less than 1, the formula to be used is given as;

    Sn = a (1-rⁿ) / 1-r

    n is the number of terms of the series

    a is the first term

    r is the common ratio.

    Sn is the sum of the series

    Given n = 3, r = 2/3 and Sn = 171,

    a=?

    Substituting this values in the formula we have;

    171 = a{1 - (2/3) ³}/1-2/3

    171 = a{1-8/27} / (1/3)

    171 = a (19/27) / (1/3)

    171 = 19a/27 * 3/1

    171 = 57a/27

    57a = 171*27

    57a = 4,617

    a = 4,617/57

    a = 81

    The first term of the series is 81
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