Решебник по алгебре 9 класс Мерзляк Задание 836

\[\boxed{\mathbf{836\ (836).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ c_{4} = \frac{1}{98};\ \ q = \frac{2}{7};\ \ \]

\[c_{4} = c_{1} \cdot q³\ \]

\[c_{1} = \frac{c_{4}}{q^{3}} = \frac{1}{98} \cdot \left( \frac{7}{2} \right)^{3} = \frac{1}{98} \cdot \frac{343}{8} =\]

\[= \frac{343}{98 \cdot 8} = \frac{7}{16}\]

\[Ответ:c_{1} = \frac{7}{16}.\]

\[2)\ c_{6} = 100,\ \ c_{9} = 100\ 000\]

\[\left\{ \begin{matrix} c_{1} \cdot q^{5} = 100\ \ \ \ \ \ \ \ \ \\ c_{1} \cdot q^{8} = 100\ 000 \\ \end{matrix} \right.\ \ \ \ \ \ \ \ |\ (\ :)\]

\[\ \frac{c_{1} \cdot q^{8}}{c_{1} \cdot q^{5}} = \frac{100\ 000}{100}\text{\ \ }\]

\[q^{3} = 1000 \Longrightarrow \ \ q = 10\]

\[c_{6} = c_{1} \cdot q^{5} \Longrightarrow \ c_{1} = \frac{c_{6}}{q^{5}} =\]

\[= \frac{100}{100000} = 0,001.\]

\[Ответ:c_{1} = 0,001.\]