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Giải bài 50 trang 57 sách bài tập toán 11 - Cánh diều

Tổng 20 số tự nhiên liên tiếp chia hết cho 3 tính từ số 3 là:

🥀Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

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

Tổng 20 số tự nhiên liên tiếp chia hết cho 3 tính từ số 3 là: A. 1320                          B. 660                  C. 630                  D. 1260

Phương pháp giải - Xem chi tiết

Xét dãy số gồm 20 số tự nhiên liên tiếp chia hết cho 3 tính từ số 3. Ta nhận thấy dãy số này là cấp số cộng với số hạng đầu \({u_1} = 3\) và công sai \(d = 3\). Sử dụng công thức \({S_n} = \frac{{\left[ {2{u_1} + \left( {n - 1} \right)d} \right]n}}{2}\) để tính tổng 20 số hạng của dãy số này.

Lời giải chi tiết

Xét dãy số gồm 20 số tự nhiên liên tiếp chia hết cho 3 tính từ số 3.Nếu viết dưới dạng liệt kê, thì dãy số đó được viết là 3, 6, 9, 12, …Ta nhận thấy dãy số này là cấp số cộng với số hạng đầu \({u_1} = 3\) và công sai \(d = 3\).Do đó, tổng 20 số hạng của dãy số này là:\({S_{20}} = \frac{{\left[ {2{u_1} + 19d} \right]20}}{2} = 10\left( {2.3 + 19.3} \right) = 630\)

Đáp án đúng là C.

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