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25 May, 20:32

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170.

What is the first term of the series?

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  1. 25 May, 21:44
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    Answer: the first term of the series is 128

    Step-by-step explanation:

    In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

    Sn = a (1 - r^n) / (1 - r)

    Where

    n represents the number of term in the sequence.

    a represents the first term in the sequence.

    r represents the common ratio.

    From the information given,

    r = 1/4 = 0.25

    n = 4

    S4 = 170

    Therefore, the expression for the sum of the 4 terms, S4 is

    170 = a (1 - 0.25^4) / (1 - 0.25)

    170 = a (1 - 0.00390625) / (1 - 0.25)

    170 = a (0.99609375) / (0.75)

    170 = 1.328125a

    a = 170/1.328125

    a = 128
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