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Консультация № 168685
01.06.2009, 15:32
0.00 руб.
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Задача про прогрессии.
Дана арифметическая прогрессия с первым членом равным 3 и разностью 4, а также геометрическая прогрессия с первым членом 1 и знаменателем 3. Найти сумму первых 3-х совпавших членов прогрессий.
Дана арифметическая прогрессия с первым членом равным 3 и разностью 4, а также геометрическая прогрессия с первым членом 1 и знаменателем 3. Найти сумму первых 3-х совпавших членов прогрессий.
Обсуждение
Неизвестный
01.06.2009, 15:47
общий
это ответ
Здравствуйте, Тимофеев Дмитрий Николаевич!
a(1)=3, d=4 прогрессия 3,7,11,...
b(1)=1, q=3 прогрессия 1,3,9,27,81,243,...
найдем совпадающие члены прогрессий a(k)=b(n)
проверять будем по b
b(2)=a(n), n=?, где n-натуральное число решение b(2)=a(1) - 1-е совпадение
b(3)=a(n), n=?, 9=3+4*(n-1) - нет решений в натуральных числах
b(4)=a(n), n=?, 27=3+4*(n-1) => n=7 b(4)=a(7) - 2-е совпадение
b(5)=a(n), n=?, 81=3+4*(n-1) - нет решений в натуральных числах
b(6)=a(n), n=?, 243=3+4*(n-1) => n=61 b(6)=a(61) - 3-е совпадение
3+27+243=273
a(1)=3, d=4 прогрессия 3,7,11,...
b(1)=1, q=3 прогрессия 1,3,9,27,81,243,...
найдем совпадающие члены прогрессий a(k)=b(n)
проверять будем по b
b(2)=a(n), n=?, где n-натуральное число решение b(2)=a(1) - 1-е совпадение
b(3)=a(n), n=?, 9=3+4*(n-1) - нет решений в натуральных числах
b(4)=a(n), n=?, 27=3+4*(n-1) => n=7 b(4)=a(7) - 2-е совпадение
b(5)=a(n), n=?, 81=3+4*(n-1) - нет решений в натуральных числах
b(6)=a(n), n=?, 243=3+4*(n-1) => n=61 b(6)=a(61) - 3-е совпадение
3+27+243=273
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