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12 June, 11:47

Find the sum of the geometric sum: 12 36 108 ... 78,732

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  1. 12 June, 12:36
    0
    Ok, geometric

    seems to be multiply by 3 each time

    hmm, so

    the sum of a geometric sequence where a1 is the first term, n is which term and r=common ratio

    Sn=a1 (1-r^n) / (1-r)

    so

    we need to find which term

    so

    an=a1 (r) ^ (n-1)

    a1=first term=12

    and common ratio is 3=r

    and the nth term is 78732

    78732=12 (3) ^ (n-1)

    78732=12 (1/3) (3^n)

    78732=4 (3^n)

    divide both sides by 4

    19683=3^n

    use math to solve and get

    9=n

    so that was the 9th term

    a1=12

    r=3

    n=9

    S9=12 (1-3^9) / (1-3)

    S9=12 (1-19683) / (-2)

    S9=-6 (-19682)

    S9=118092

    the sum is 118092
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