Answer:
Step-by-step explanation:
[tex]a_{n}=a_{1}*r^{n-1}\\\\a_{3} = 15[/tex]
[tex]a_{1}*r^{3-1}=15\\\\a_{1}r^{2}=15 -------------------------------------(I)\\\\a_{6} = \frac{5}{27}\\\\a_{1} *r^{6-1}=\frac{5}{27}\\\\a_{1}r^{5}=\frac{5}{27}-----------------------(II)\\[/tex]
(II) ÷ (I)
[tex]\frac{a_{1}r^{5}}{a_{1}r^{2}}=\frac{\frac{5}{27}}{15}\\\\\\r^{3}=\frac{5}{27}*\frac{1}{15}\\\\r^{3}=\frac{1}{27*3}\\\\r^{3}=\frac{1}{81}\\\\r=\frac{1}{3\sqrt{3}}[/tex]
