Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises - Page 1034: 32

$r=\dfrac {1}{3};a_{1}=2700$

$\dfrac {a_{m}}{a_{n}}=r^{m-n}\Rightarrow \dfrac {a_{g}}{a_{3}}=r^{6}=\dfrac {\dfrac {100}{243}}{300}=\dfrac {1}{729}\Rightarrow r=\dfrac {1}{3};a_{3}=a_{1}\times r^{2}\Rightarrow 300=a_{1}\times \left( \dfrac {1}{3}\right) ^{2}\Rightarrow a_{1}=2700$