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16 March, 05:32

Find the thirteenth term of a geometric sequence that has a first term of 4,096 and a common ratio of 1/2 (one-half).

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  1. 16 March, 07:43
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    Let's create a function for this geometric sequence. The general form of the function will be:

    f (x) = C*R^x

    where

    C is some constant

    R = ratio of sequential terms

    x = term number.

    We've been given 1/2 as the ratio. So we have:

    f (x) = C*0.5^x

    We've also been told that the first term is 4096. So we have

    f (x) = C*0.5^x

    4096 = C*0.5^1

    Now let's solve for C

    4096 = C*0.5^1

    4096 = C*0.5

    8192 = C

    So our function is

    f (x) = 8192*0.5^x

    Let's solve for x = 13

    f (x) = 8192*0.5^x

    f (13) = 8192*0.5^13

    f (13) = 8192*0.0001220703125

    f (13) = 1
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