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Bài 7 trang 56 SGK Toán 11 tập 1 - Chân trời sáng tạo

Khi một vận động viên nhảy dù nhảy ra khỏi máy bay, gia sử quãng đường người ấy rơi tự do (tính theo feet) trong mỗi giây liên tiếp theo thứ tự trước khi bung dù lần lượt là:

T♔ổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trꦡời sáng tạo

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

Khi một vận động viên nhảy dù nhảy ra khỏi máy bay, gia sử quãng đường người ấy rơi tự do (tính theo feet) trong mỗi giây liên tiếp theo thứ tự trước khi bung dù lần lượt là: 16; 48; 80; 112; 144; ... (các quãng đường này tạo thành cấp số cộng). a) Tính công sai của cấp số cộng trên. b) Tính tổng chiều dài quãng đường rơi tự do của người đó trong 10 giây đầu tiên.

Phương pháp giải - Xem chi tiết

‒ Chứng minh các số hạng liên tiếp nhau hơn kém nhau cùng một số không đổi. ‒ Sử dụng công thức tính tổng \(n\) số hạng đầu tiên của cấp số cộng có số hạng đầu \({u_1}\) và công sai \(d\) là: \({S_n} = \frac{{n\left( {{u_1} + {u_n}} \right)}}{2} = \frac{{n\left[ {2{u_1} + \left( {n - 1} \right)d} \right]}}{2}\).

Lời giải chi tiết

a) Ta có:\(48 = 16 + 32;80 = 48 + 32;112 = 80 + 32;144 = 112 + 32;...\)Vậy dãy số trên là cấp số cộng có số hạng đầu \({u_1} = 16\) và công sai \(d = 32\).b) Tổng chiều dài quãng đường rơi tự do của người đó trong 10 giây đầu tiên là:\({S_{10}} = \frac{{10\left[ {2{u_1} + \left( {10 - 1} \right)d} \right]}}{2} = \frac{{10\left( {2{u_1} + 9d} \right)}}{2} = \frac{{10\left( {2.16 + 9.32} \right)}}{2} = 1600\) (feet)

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