how to solve math questions

how to solve what is the sum of the first ten terms of the geometric sequence 4,8,16,.....?

$\begin{array}{rcl} a_1 &=& 2^2 \\ a_2 &=& 2^3 \\ a_3 &=& 2^4 \\ \cdots \\ a_n &=& 2^{n+1} \end{array}$

 $\begin{array}{rcrcl} s_n &=& a_1 &+& a_2+a_3+a_4+ \cdots + a_{n-1} + a_n \\ \hline s_n &=& 2^2 &+& 2^3+2^4+2^5+ \cdots + 2^n + 2^{n+1} \\ 2\cdot s_n &=& && 2^3+2^4+2^5+ \cdots + 2^n+2^{n+1} + 2^{n+2} \\ \hline s_n - 2\cdot s_n &=& 2^2 - 2^{n+2} \\ s_n(1 - 2) &=& 2^2 - 2^{n}\cdot 2^2 \\ -s_n &=& 2^2 - 2^{n}\cdot 2^2 \\ s_n &=& 2^{n}\cdot 2^2 - 2^2\\ s_n &=& 2^2\cdot (2^{n}-1)\\\\ \mathbf{s_n} &\mathbf{=}& \mathbf{4\cdot (2^{n}-1)} \\\\ s_{10} &=& 4\cdot (2^{10}-1)\\ s_{10} &=& 4\cdot (1024-1)\\ s_{10} &=& 4\cdot 1023\\ \mathbf{s_{10}} &\mathbf{=} & \mathbf{4092} \end{array}$

The sum of the first ten terms of the geometric sequence is 4092