Which term of the progression $18,-12,8,--$ -- is $\frac{512}{729}$ ?

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Professor PC Thomas Classes · Answer

$a=18$, $r = -\frac{12}{18} = -\frac{2}{3}$. $18(-2/3)^{n-1} = \frac{512}{729} \implies (-2/3)^{n-1} = \frac{256}{6561} = (-2/3)^8 \implies n-1 = 8 \implies n = 9$.