Question

Determine if the sequence is geometric. If it is, find the explicit formula and recursive formula.

3,18,108,648

Answer 1

`a_1=3;\ a_2=18;\ a_3=108;\ a_4=648\\\\if\ a_n\ is\ a\ geometric\ sequance\ then\ (a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)\\\\check:\\\\(a_2)/(a_1)=(18)/(3)=6\\\\(a_3)/(a_2)=(108)/(18)=6\\\\(a_4)/(a_3)=(648)/(108)=6\\\\correct!\\\\It's\ a\ geometric\ sequence`


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