The sum to infinity of a G.P is 20 and the sum of their squares is 100 . Then the first term of the

Question

The sum to infinity of a G.P is 20 and the sum of their squares is 100 . Then the first term of the G.P is

Professor PC Thomas Classes · Answer

$ \begin{aligned} & \frac{a}{1-r}=20, \frac{a^2}{1-r^2}=100 \ & a=20(1-r), \frac{400(1-r)^2}{1-r^2}=100 \ & \frac{4(1-r)}{1+r}=1,4(1-r)=1+r \ & 3=5 r, r=\frac{3}{5} \ & a=20\left(1-\frac{3}{5}ight)=8 \end{aligned} $