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2015-07-17T18:37:32+08:00

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Since these are terms of a geometric sequence, they have a common ratio so:
 \frac{5x+1}{x+2} = \frac{x+11}{5x+1}  \\ 25x^2+10x+1=x^2+13x+22 \\24x^2-3x-21=0 \\ 8x^2-x-7=0 \\ (8x+7)(x-1)=0

Therefore x can be equal to -7/8 or 1.

The sum of n terms in a geometric sequence is equal to  \frac{a_1(r^n-1)}{r-1}

When x = -7/8, the first term would be 9/8 and the common ratio would be -3.
The sum of the first ten terms would be:
( \frac{9}{8})[(-3)^{10}-1]/(-3-1) \\ =( \frac{9}{8})( 59,048)/-4 \\ =-16,607.25

When x = 1, the first term would be 3 and the ratio would be 2.
3(2^{10}-1)/(2-1) \\ =3(1023)/1 \\ =3069

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