Пример №36 из задания 20

Среднее арифметическое \(5\) различных натуральных чисел равно \(7\). Среднее арифметическое этих чисел и шестого числа равно \(8\). Чему равно шестое число? 


Решение

По условию, среднее арифметическое \(5\) различных натуральных чисел равно \(7\):

\(\frac{a_1+a_2+…+a_5}{5}=7\).

Значит, сумма первых \(5\) чисел будет равна \(5⋅7=35\).

Среднее арифметическое этих чисел (первых пяти, т.е. \(35\)) и шестого числа равна \(8\):

\(\frac{35+a_6}{6}=8\);

\(a_6=8⋅6-35=13\).

Получилось, что шестое число равно \(13\).

Ответ: \(13\).


Источник: ЕГЭ 2021. Математика. Базовый уровень. 50 вариантов. Типовые варианты экзаменационных заданий. (вариант №10) (Купить книгу)

Пример №36 из задания 20: 37 комментариев

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