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Determine if the sequence is geometric. If it is, find the explicit formula and recursive formula.
3,18,108,648

Sagot :

[tex]a_1=3;\ a_2=18;\ a_3=108;\ a_4=648\\\\if\ a_n\ is\ a\ geometric\ sequance\ then\ \frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}\\\\check:\\\\\frac{a_2}{a_1}=\frac{18}{3}=6\\\\\frac{a_3}{a_2}=\frac{108}{18}=6\\\\\frac{a_4}{a_3}=\frac{648}{108}=6\\\\correct!\\\\It's\ a\ geometric\ sequence[/tex]

[tex]The\ formula\ of\ geometric\ sequence:a_n=a_1r^{n-1}\\\\a_1=3;\ r=\frac{a_2}{a_1}=6\\\\therefore\\\\a_1=3\cdot6^{n-1}=3\cdot6^n\cdot6^{-1}=3\cdot6^n\cdot\frac{1}{6}=3\cdot\frac{1}{6}\cdot6^n=\boxed{\frac{1}{2}\cdot6^n}[/tex]
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