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`