A recursive rule for a geometric sequence
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
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[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]
