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23 August, 05:23

What is the sum of the first ten terms in the geometric series 4 - 12 + 36 - 108 + ... ?

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  1. 23 August, 05:27
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    This is a geometric

    first term is a = 4

    2nd term is mult by 3 to give us 4 (31)

    3rd term is 4 (32)

    4rth term is 4 (33)

    and the 12th term is 4 (311)

    so a is 4 and the common ratio (r) is equal to 3

    that's all you need to know.

    The formula for the sum of the 12 terms in geometric is:

    S (n) = a (1-rn1-r)

    substituting a=4 and r=3, we get:

    s (12) = 4 (1-3121-3) or a total sum of 1,062,880.

    you can confirm this formula is true by calculating the sum of the first 4 terms and comparing s (4) = 4 (1-341-3)

    All you have to do is figure out what the first term is and then figure out the common ratio between them!
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