ГДЗ по алгебре 9 класс Мерзляк Задание 801

\[\boxed{\mathbf{801\ (801).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = 100;\ \ S_{6} = 5 \cdot S_{7 - 12}\]

\[S_{6} = \frac{2cc + 5d}{2} \cdot 6 =\]

\[= (2 \cdot 100 + 5d) \cdot 3 =\]

\[= (200 + 5d) \cdot 3\]

\[(200 + 5d) \cdot 3 = 5 \cdot S_{7 - 12}\]

\[S_{7 - 12} = \frac{2a_{7} + 5d}{2} \cdot 6 =\]

\[= \left( 2 \cdot \left( a_{1} + 6d \right) + 5d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 12d + 5d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 17d \right) \cdot 3 =\]

\[= (200 + 17d) \cdot 3\]

\[(200 + 5d) \cdot 3 =\]

\[= 5 \cdot (200 + 17d) \cdot 3\ \ \ \ \ |\ :3\]

\[200 + 5d = 1000 + 85d\]

\[80d = - 800,\ \ d = - 10\]

\[Ответ:\ d = - 10.\]