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Giải bài 9 trang 65 sách bài tập toán 11 - Chân trời sáng tạo tập 1

Một tháp 10 tầng có diện tích sàn của tầng dưới cùng là \(6\;144{m^2}\). Tính diện tích mặt sàn tầng trên cùng, biết rằng diện tích mặt sàn mỗi tầng bằng nửa diện tích mặt sàn tầng ngay bên dưới.

ꦕTổng 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 tháp 10 tầng có diện tích sàn của tầng dưới cùng là \(6\;144{m^2}\). Tính diện tích mặt sàn tầng trên cùng, biết rằng diện tích mặt sàn mỗi tầng bằng nửa diện tích mặt sàn tầng ngay bên dưới.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về số hạng tổng quát của cấp số nhân để tính: Nếu một cấp số nhân \(\left( {{u_n}} \right)\) có số hạng đầu \({u_1}\) và công bội q thì số hạng tổng quát \({u_n}\) của nó được xác định bởi công thức: \({u_n} = {u_1}.{q^{n - 1}},n \ge 2\). 

Lời giải chi tiết

Gọi diện tích mặt sàn tầng n là \({u_n}\left( {n \in \mathbb{N}*} \right)\). Dãy \(\left( {{u_n}} \right)\) lập thành một cấp số nhân có số hạng đầu \({u_1} = 6\;144\) và công bội \(q = \frac{1}{2}\). Do đó, số hạng tổng quát của dãy số là: \({u_n} = 6\;144.{\left( {\frac{1}{2}} \right)^{n - 1}}\). Diện tích mặt sàn tầng trên cùng là: \({u_{10}} = {u_1}.{q^9} = 6\;144.{\left( {\frac{1}{2}} \right)^9} = 12\left( {{m^2}} \right)\) Vậy diện tích mặt sàn tầng trên cùng là \(12{m^2}\).

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