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26 July, 19:54

Describe an infinite geometric series with the beginning value of 2 that converges to 10 what are the first four terms of the series

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  1. 26 July, 23:35
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    an = 2· (4/5) ^ (n-1) 2, 8/5, 32/25, 128/125

    Step-by-step explanation:

    The sum of an infinite geometric series is ...

    S = a1 / (1 - r)

    where r is the common ratio. The sum will only exist if |r| < 1.

    The problem statement tells us S = 10 and a1 = 2, so we have ...

    10 = 2 / (1 - r)

    r = 1 - 2/10 = 4/5

    So the n-th term of the series is ...

    an = a1·r^ (n-1)

    an = 2· (4/5) ^ (n-1)

    For values of n = 1 to 4, the terms are ...

    2, 8/5, 32/25, 128/125
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