[tex]a_2=20\\a_4=5\\S_{10} = ?\\\\a_2=a_1*q\\20=a_1=q /:q\\\frac{20}q=a_1\\\\a_4=a_1*q^3\\5=\frac{20}q*q^3\\5=20*q^2 /:20\\\frac5{20}=q^2\\q=\sqrt{\frac5{20}}=\frac{\sqrt5}{2\sqrt{5}}=\frac12\\\\S_n=a_1*\frac{1-q^n}{1-q}\\\\a_1=\frac{20}{\frac12}=20:\frac12=20*2=40\\\\S_{10}=40*\frac{1-(\frac12)^{10}}{1-\frac12}\\S_{10}=40*\frac{1-\frac{1}{1024}}{\frac12}\\S_{10}=80*(1-\frac1{1024})\\S_{10}=80*\frac{1023}{1024}=\frac{81840}{1024}=79\frac{944}{1024}=79\frac{59}{64}[/tex]
