Question

What is the fifth term of a sequence whose first term is 5 and whose common ratio is 3

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=5\\ r=3\\ n=5 \end{cases} \\\\\\ a_n=5\cdot 3^{n-1}\implies a_5=5\cdot 3^{5-1} \\\\\\ a_5=5\cdot 3^4\implies a_5=5\cdot 81\implies a_5=405$