evanmskroch
14

# Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively

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MickieGelormino111

$a_2=-12;\ a_5=768\\\\a_n=a_1r^{n-1}\\\\a_5:a_2=r^3\\\\r^3=768:(-12)\\\\r^3=-64\\\\r=\sqrt[3]{-64}\\\\r=-4\\\\a_1=a_2:r\to a_1=-12:(-4)=3\\\\\boxed{a_n=3\cdot(-4)^{n-1}}$

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