Zadanie 5
a_1=\frac{2}{3}
a_4=\frac{3}{2}
a_1*q^3=a_4
\frac{2}{3}*q^3=\frac{3}{2}|:\frac{2}{3}
q^3=\frac{3}{2}*\frac{3}{2}
q^3=\frac{9}{4}\\\\q = \sqrt[3]{\frac{9}{4}}\\\\a_n=a_1*q^{n-1}\\\\a_n=\frac{2}{3}*(\frac{\sqrt[3]{9}}{\sqrt[3]{4}})^{n-1}\\\\a_n=\frac{2}{3}*(\frac{\sqrt[3]{9}* \sqrt[3]{2}}{\sqrt[3]{4} * \sqrt[3]{2}})^n * (\frac{\sqrt[3]{9}}{\sqrt[3]{4}})^{-1}\\\\a_n=\frac{2}{3}* (\frac{\sqrt[3]{18}}{2})^n * \frac{\sqrt[3]{4}}{\sqrt[3]{9}}\\\\a_n=\frac{2}{3} * (\frac{\sqrt[3]{18}}{2})^n * \frac{\sqrt[3]{4}*\sqrt[3]{3}}{\sqrt[3]{9} * \sqrt[3]{3}}\\\\a_n=\frac{2}{3} * (\frac{\sqrt[3]{18}}{2})^n * \frac{\sqrt[3]{12}}{3}\\\\a_n=\frac{2\sqrt[3]{12}}{9} * (\frac{\sqrt[3]{18}}{2})^n <-- odpowiedź