2. The first term of the geometric progression $b_{1}=\sqrt{3}$, the fifth term $b_{5}=\sqrt{243}$. Find the sixth term and the common ratio of the progression.
Solution: $b_{1}=\sqrt{3} ; b_{5}=\sqrt{243}, b_{6}=$ ? $q=$ ?

$b_{5}=b_{1} \cdot q^{4}=\sqrt{3} \cdot q^{4}=\sqrt{243} \Rightarrow q^{4}=\sqrt{\frac{243}{3}}=3^{2} ; q= \pm \sqrt{3}, b_{6}=\sqrt{243} \cdot q= \pm \sqrt{81 \cdot 3^{2}}= \pm 27$.

Answer: $b_{6}= \pm 27$