Question

Determine if the sequence 9,18,36 is geometric or arithmetic.write an explicit formula

Answer 1

9                             18                        36

                             9 * 2                     18 * 2

so notice, to get the next term, we simply multiply the "current" one by 2, namely is a geometric sequence, with a "common ratio" of 2, and we know the first term's value is 9.

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=9\\ r=2 \end{cases}\implies a_n=9\cdot 2^{n-1}$