The common ratio is 5. So we have
\(S\)
\(= 2 + 10 + 50 + \cdots + 2\cdot 5^n\)
\(- \qquad 5S\)
\(= ~~~~~~10 + 50 + \cdots + 2\cdot 5^n + 2\cdot5^{n+1}\)
\(-4S\)
\(= 2 - 2\cdot5^{n+1}\)
Thus
\(S = \dfrac{2-2\cdot 5^{n+1}}{-4}\)