Question

Determine 7th term in the geometric sequence whose first term is 5 and whose common ratio is 2.

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=5\\ r=2\\ n=7 \end{cases} \\\\\\ a_7=5\cdot 2^{7-1}\implies a_7=5\cdot 2^6\implies a_7=320$