[tex]a_2=25\\a_3=10\\\\a_2*q=a_3\\25*q=10 /:25\\q=\frac{10}{25}=\frac25\\\\a_1*q=a_2\\a_1*\frac25=25 /*\frac52\\a_1=\frac{125}2\\\\S_6=a_1*\frac{1-q^6}{1-q}\\\\S_6=\frac{125}2*\frac{1-(\frac25)^6}{1-\frac25}\\S_6=\frac{125}2*\frac{1-\frac{64}{15625}}{\frac35}\\S_6=\frac{125}2*\frac{15561}{15625}*\frac53\\S_6=\frac{1}2*\frac{5187}{25}*\frac11\\S_6=\frac{5187}{50}=103.74[/tex]
