Question

Find the fifth term of the geometric sequence whose first term is 81 and whose common ratio is 1/3.(1 point)13

Answer 1

$n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{5}\\ a_1=\stackrel{\textit{first term}}{81}\\ r=\stackrel{\textit{common ratio}}{\frac{1}{3}} \end{cases}\implies a_5=81\left( \cfrac{1}{3} \right)^{5-1} \\\\\\ a_5=81\left( \cfrac{1}{3} \right)^4\implies a_5=81\cdot \cfrac{1}{81}\implies a=1$