Страница 99 номер 252, ГДЗ по алгебре за 9 класс к учебнику Алимова с ответами и решением
Найти сумму \(n\) первых членов арифметической прогрессии, если: 1) \(a_1 = 1\), \(a_n = 20\), \(n = 50\); 2) \(a_1 = 1\), \(a_n = 200\), \(n = 100\); 3) \(a_1 = -1\), \(a_n = -40\), \(n = 20\); 4) \(a_1 = 2\), \(a_n = 100\), \(n = 50\).
1) \(a_{1} = 1\), \(a_{n} = 20\), \(n = 50\)
\(S_{n} = \dfrac{\left(a_{1} + a_{n}\right) \cdot n}{2}\)
\(S_{n} = \dfrac{\left(1 + 20\right) \cdot 50}{2} = 25 \cdot 21 = 525\)
2) \(a_{1} = 1\), \(a_{n} = 200\), \(n = 100\)
\(S_{n} = \dfrac{\left(a_{1} + a_{n}\right) \cdot n}{2}\)
\(S_{n} = \dfrac{\left(1 + 200\right) \cdot 100}{2} = 50 \cdot 201 = 10050\)
3) \(a_{1} = -1\), \(a_{n} = -40\), \(n = 20\)
\(S_{n} = \dfrac{\left(a_{1} + a_{n}\right) \cdot n}{2}\)
\(S_{n} = \dfrac{\left(-1 - 40\right) \cdot 20}{2} = 10 \cdot \left(-41\right) = -410\)
4) \(a_{1} = 2\), \(a_{n} = 100\), \(n = 50\)
\(S_{n} = \dfrac{\left(a_{1} + a_{n}\right) \cdot n}{2}\)
\(S_{n} = \dfrac{\left(2 + 100\right) \cdot 50}{2} = 25 \cdot 102 = 2550\)
