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Giải bài 30 trang 54 sách bài tập toán 11 - Cánh diều

Trong các dãy số sau, dãy số nào là cấp số nhân?

♎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

Trong các dãy số sau, dãy số nào là cấp số nhân? A. \(128; - 64;{\rm{ 32;}} - 16;{\rm{ 8}}\)                             B. \(\sqrt 2 ;{\rm{ 2; 2}}\sqrt 2 ;{\rm{ 4; 8}}\) C. \(5;{\rm{ 6; 7; 8; 9}}\)                                              D. \(15;{\rm{ 5; 1; }}\frac{1}{5};{\rm{ }}\frac{1}{{25}}\)

Phương pháp giải - Xem chi tiết

Dãy số \(\left( {{u_n}} \right)\) là cấp số nhân khi thương \(\frac{{{u_{n + 1}}}}{{{u_n}}}\) không đổi với mọi \(n \ge 1\) và \({u_n} \ne 0\).

Lời giải chi tiết

a) Dãy số \(128; - 64;{\rm{ 32;}} - 16;{\rm{ 8}}\) 🦂là cấp số nhân vì \(\frac{{ - 64}}{{128}} = \frac{{32}}{{ - 64}} = \frac{{ - 16}}{{32}} = \frac{8}{{ - 16}} = \frac{{ - 1}}{2}\)

b) Dãy số \(\sqrt 2 ;{\rm{ 2; 2}}\sqrt 2 ;{\rm{ 4; 8}}\) ꦜkhông là cấp số nhân vì \(\frac{4}{{2\sqrt 2 }} = \sqrt 2 \) và \(\frac{8}{4} = 2\).

c) Dãy số \(5;{\rm{ 6; 7; 8; 9}}\) ☂không là cấp số nhân vì \(\frac{6}{5} \ne \frac{7}{6}\).

d) Dãy số \(15;{\rm{ 5; 1; }}\frac{1}{5};{\rm{ }}\frac{1}{{25}}\) không là cấp số nhân vì \(\frac{5}{{15}} = \frac{1}{3} \ne \frac{1}{5}\).Đáp án đúng là A.

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