Question

What is the explicit rule for the nth term of the geometric sequence? Thanks

Answer 1

Solution.

Given the sequence

`3,18,108,648,3888`

Test which kind of sequence it is

`\begin{gathered} (18)/(3)=6 \\ (108)/(18)=6 \\ The\text{ sequence has a common ratio which is 6. } \\ Thus,\text{ it is a geometric sequence} \\ \end{gathered}`
`\begin{gathered} The\text{ nth term of a geometric sequence can be determined by the formula} \\ a_n=ar^(n-1) \\ where\text{ a = 1st term} \\ r=common\text{ ratio} \end{gathered}`
`a_n=3(6^(n-1))`
`The\text{ answer is a}_n=3(6^(n-1))`