\[\boxed{\mathbf{837\ (837).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[2,\ 6,\ 18,\ \ldots,\ 486,\ \ldots\]
\[q = \frac{6}{2} = 3\]
\[486 = b_{1}q^{n - 1}\ \]
\[486 = 2 \cdot 3^{n - 1}\text{\ \ }\]
\[3^{n - 1} = 243\ \ \]
\[3^{n - 1} = 3^{5}\]
\[n - 1 = 5 \Longrightarrow \ \ n = 6\]
\[Ответ:n = 6.\]