Answer 1

\[S_{11} = \sum\nolimits_{n = 1}^{11} \left( 2 + 3^n \right)\]

\[ \Rightarrow S_{11} = \sum\nolimits_{n = 1}^{11} 2 + \sum\nolimits_{n = 1}^{11} 3^n \]

\[ \Rightarrow S_{11} = 2 \times 11 + \left( 3 + 3^2 + 3^3 + . . . + 3^{11} \right)\]

\[ = 22 + 3\left( \frac{3^{11} - 1}{3 - 1} \right) \]

\[ = 22 + \left( \frac{177147 - 1}{2} \right)\]

\[ = 22 + 265719 \]

\[ = 265741\]