Question

Find a₇ of the geometric sequence where a₁ is 11 and the common ratio is 5.

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=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=11\\ r=5\\ n=7 \end{cases} \\\\\\ a_7=11\cdot 5^(7-1)\implies a_7=11\cdot 5^6\implies a_7=171875`