Question

Find the sixth term of the geometric sequence 9, 18, 36, ...

Answer 1

Answer:

This is a geometric sequence because any term divided by the previous term is a constant called the common ratio. r=36/18=18/9=2 A geometric sequence is expressed as

\begin{gathered}a_n=ar^{n-1},\text{ where a=initial term, r=common ratio, n=term number}\\ \\ a_n=9(2^{n-1})\\ \\ a_6=9(2^5)\\ \\ a_6=288\end{gathered}an=arn−1, where a=initial term, r=common ratio, n=term numberan=9(2n−1)a6=9(25)a6=288