ГДЗ по алгебре 9 класс Макарычев Задание 705

\[\boxed{\text{705\ (705).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ b_{1} = \frac{243}{256},\ \ q = \frac{2}{3},\ \ \]

\[n = 8;\]

\[b_{8} = b_{1} \cdot q^{7} = \frac{243}{256} \cdot \left( \frac{2}{3} \right)^{7} =\]

\[= \frac{3^{5}}{2^{8}} \cdot \frac{2^{7}}{3^{7}} = \frac{1}{18}\text{.\ }\]

\[\textbf{б)}\ b_{1} = \sqrt{\frac{2}{3}},\ \ q = - \sqrt{6},\]

\[n = 5;\]

\[b_{5} = b_{1} \cdot q^{4} = \sqrt{\frac{2}{3}} \cdot \left( - \sqrt{6} \right)^{4} =\]

\[= 36 \cdot \sqrt{\frac{2}{3}} = 12\sqrt{6}.\]