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27 October, 21:07

The sum of the first 333 terms of a geometric series is 171171171 and the common ratio is / dfrac23

3

2



start fraction, 2, divided by, 3, end fraction.

What is the first term of the series?

+3
Answers (1)
  1. 28 October, 00:04
    0
    The first term of the series is 81

    Step-by-step explanation:

    The sum of the nth term of a geometric sequence is expressed as shown;

    Sn = a (1-rⁿ) / 1-r for r<1

    a is the first term

    r is the common ratio

    n is the number of terms

    Given Sn = 171

    r = 2/3

    n = 3

    a = ?

    Substituting the values in the equation

    171 = a (1 - (2/3) ³) / 1-2/3

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

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

    171 = a * 19/27 * 3/1

    171 = a * 19/9

    Cross multiplying

    171*9 = 19a

    1539 = 19a

    a = 1539/19

    a = 81

    The first term is 81
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