Решебник по алгебре 9 класс Мерзляк Задание 874

\[\boxed{\mathbf{874\ (874).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ c_{4} = 216;\ \ q = - 3:\]

\[c_{4} = c_{1}q^{3}\ \]

\[c_{1} = \frac{c_{4}}{q^{3}} = \frac{216}{( - 3)^{3}} = - \frac{216}{27} = - 8.\]

\[S_{6} = \frac{- 8 \cdot \left( ( - 3)^{6} - 1 \right)}{- 3 - 1} =\]

\[= \frac{- 8 \cdot (729 - 1)}{- 4} = 2 \cdot 728 =\]

\[= 1456.\]

\[2)\ c_{1} = 5\sqrt{5};\ \ c_{5} = 125\sqrt{5};\ \ \]

\[q > 0\]

\[c_{5} = c_{1}q^{4}\]

\[q^{4} = \frac{c_{5}}{c_{1}} = \frac{125\sqrt{5}}{5\sqrt{5}} =\]

\[= 25 \Longrightarrow \ q = \sqrt{5}.\]

\[S_{6} = \frac{5\sqrt{5} \cdot \left( \left( \sqrt{5} \right)^{6} - 1 \right)}{\sqrt{5} - 1} =\]

\[= \frac{5\sqrt{5} \cdot (125 - 1)}{\sqrt{5} - 1} =\]

\[= \frac{5\sqrt{5} \cdot 124 \cdot \left( \sqrt{5} + 1 \right)}{\left( \sqrt{5} - 1 \right)\left( \sqrt{5} + 1 \right)} =\]

\[= \frac{620\sqrt{5} \cdot \left( \sqrt{5} + 1 \right)}{5 - 1} =\]

\[= 155 \cdot \left( 5 + \sqrt{5} \right).\]