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March 28, 2017

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The first term of an arithmetic sequence is 2. The first, third and eleventh terms are the first three terms of a geometric sequence. Determine the seventh term of the geometric sequence

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    AS: 2 ... 2+2d ... 2+10d
    GS: a ar ar^2

    a = 2
    ar = 2+2d -- r = 1+d
    ar^2 = 2+10d = 2r*r

    2+10d = 2(1+d)^2
    d = 3

    AS: 2 5 8 11 14 17 20 23 26 29 32 . . .
    GS: 2 8 32 128 512 2048 8192 . . .

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