Решебник по алгебре 9 класс Мерзляк Задание 724

\[\boxed{\mathbf{724\ (724).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ - 5,\ - 7,\ - 9,\ - 11,\ldots\]

\[a_{1} = 5;\ \ \ d = - 7 - ( - 5) = 2\]

\[\ a_{n} = a_{1} + d(n - 1) =\]

\[= - 5 - 2 \cdot (n - 1) =\]

\[= - 5 - 2n + 2 = - 3 - 2n\]

\[\ a_{n} = - 3 - 2n;\]

\[2)\ 2,\ 2\frac{1}{6},\ 2\frac{1}{3},\ 2\frac{1}{2},\ldots\]

\[a_{1} = 2;\ \ \ d = 2\frac{1}{6} - 2 = \frac{1}{6}\]

\[a_{n} = 2 + \frac{1}{6} \cdot (n - 1) =\]

\[= 2 + \frac{1}{6}n - \frac{1}{6} = 1\frac{5}{6} + \frac{1}{6}n\]

\[a_{n} = 1\frac{5}{6} + \frac{1}{6}n;\]

\[3)\ a²,\ 2a²,\ 3a²,\ 4a²,\ \ldots\]

\[a_{1} = a^{2};\ \ \ \ d = 2a^{2} - a^{2} = a^{2}\]

\[a_{n} = a^{2} + a^{2}(n - 1) =\]

\[= a^{2} + na^{2} - a^{2} = na^{2}\]

\[a_{n} = na^{2};\]

\[4)\ a + 3,\ a + 1,\ a - 1,\ a - 3,\ \ldots\]

\[a_{1} = a + 3;\ \ \ d = a + 1 -\]

\[- (a + 3) = a + 1 - a - 3 = - 2\]

\[\ a_{n} = a_{1} + d(n - 1),\]

\[a_{n} = a + 3 - 2 \cdot (n - 1) =\]

\[= a + 3 - 2n + 2 = a - 2n + 5.\]