Предмет:
МатематикаАвтор:
анонимДано: (an) – арифметическая прогрессия;
a4 + a7 = 6;
a5 - a2 = 12;
Найти: a2, a3 - ?
Формула n-го члена арифметической прогрессии:
an = a1 + d * (n - 1).
Выразим, согласно этой формуле, a2, a4, a5 и a7:
a2 = a1 + d,
a3 = a1 + 2d,
a4 = a1 + 3d,
a5 = a1 + 4d,
a7 = a1 + 6d.
Т.о. a4 + a7 = (a1 + 3d) + (a1 + 6d) = 2a1 + 9d = 6;
a5 - a2 = a1 + 4d – (a1 + d) = 3d = 12.
Составим и решим полученную систему уравнений:
2a1 + 9d = 6, (1)
3d = 12 (2)
Из (2) уравнения выразим d = 12 : 3 = 4.
Подставим полученное значение d в (1) уравнение системы:
2a1 + 9 * 4 = 6;
2a1 = -30;
a1 = - 15.
Подставим полученные значение a1 и d в формулы нахождения второго и третьего членов заданной прогрессии:
a2 = a1 + d = - 15 + 4 = -11,
a3 = a1 + 2d = -15 + 2 * 4 = -7.
Ответ: a2 = -11, a3 = -7.
Автор:
gretawolfДобавить свой ответ
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