$\,\frac{a}{{1\,\, – \,\,r}}\,\, = \,\,20\,\,\,..\,..\,\,(i)\,$

$\,\frac{{{a^2}}}{{1\,\, – \,\,{r^2}}}\,\, = \,\,100\,\,\,…….\,\,(ii)$

સમીકરણ $(i)$ અને સમીકરણ  $(ii)$ પરથી

$\frac{{\text{a}}}{{{\text{1}}\,\, + \,\,{\text{r}}}}\,\, = \,\,5$

$(\therefore \,\,a\,\, = \,\,20(1\,\, – \,\,r)\,by\,\,(i))$

$ \Rightarrow \,\,\frac{{20(1\,\, – \,\,r)}}{{1\,\, + \,\,r}}\,\, = \,\,5\,\,\,\,$

$ \Rightarrow \,\,5r\,\, = \,\,3\,\,\,\,\, \Rightarrow \,\,r\,\, = \,\,3/5$