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Bài 14 trang 62 SGK Toán 11 tập 1 - Chân trời sáng tạo

Một cây đàn organ có tần số âm thanh các phím liên tiếp tạo thành một cấp số nhân. Cho biết tần số phím La Trung là 400 Hz và tần số của phím La Cao cao hơn 12 phím là 800 Hz

ඣTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Một cây đàn organ có tần số âm thanh các phím liên tiếp tạo thành một cấp số nhân. Cho biết tần số phím La Trung là 400 Hz và tần số của phím La Cao cao hơn 12 phím là 800 Hz (nguồn:꧙ // vi.wikipedia.org/wiki/Organ). Tìm công bội của cấp số nhân nói trên (làm tròn kết quả đến hàng phần nghìn).

Phương pháp giải - Xem chi tiết

Sử dụng công thức số hạng tổng quát của cấp số nhân có số hạng đầu \({u_1}\) và công bội \(q\) thì số hạng tổng quát là: \({u_n} = {u_1}.{q^{n - 1}},n \ge 2\).

Lời giải chi tiết

Giả sử tần số âm thanh từ phím La Trung đến phím La Cao tạo thành một cấp số nhân có số hạng đầu \({u_1}\) và công bội \(q\).Theo đề bài ta có:\(\left\{ \begin{array}{l}{u_1} = 400\\{u_{13}} = 800\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1} = 400\\{u_1}.{q^{12}} = 800\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1} = 400\\400{q^{12}} = 800\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1} = 400\\{q^{12}} = 2\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1} = 400\\q \approx 1,059\end{array} \right.\)Vậy công bội của cấp số nhân đó là \(q \approx 1,059\).

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