三明高三數(shù)列題庫及答案

一、單項(xiàng)選擇題(每題2分,共10題)1.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_1=1\),\(a_{n+1}=2a_n+1\),則\(a_3\)的值為（）A.3B.5C.7D.92.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_2=3\),\(a_5=9\),則公差\(d\)為()A.1B.2C.3D.43.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),\(a_3=8\),則公比\(q\)為()A.2B.-2C.2或-2D.44.數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2\),則\(a_5\)的值為()A.9B.10C.11D.125.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_n=\frac{n}{n+1}\),則\(a_{10}\)的值為()A.\(\frac{10}{11}\)B.\(\frac{11}{12}\)C.\(\frac{9}{10}\)D.\(\frac{12}{13}\)6.等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=2n^2+n\),則\(a_1\)的值為()A.3B.2C.1D.07.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(a_4=8\),則\(a_2\)的值為()A.2B.-2C.4D.-48.數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_{n+1}=a_n+2\),\(a_1=1\),則\(a_{10}\)的值為()A.19B.20C.21D.229.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_3+a_7=10\),則\(a_5\)的值為()A.5B.6C.7D.810.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_2=2\),\(a_5=16\),則\(a_3\)的值為()A.4B.8C.-4D.-8二、多項(xiàng)選擇題(每題2分,共10題)1.下列數(shù)列中是等差數(shù)列的有(）A.\(1,3,5,7,\cdots\)B.\(2,4,8,16,\cdots\)C.\(1,1,1,1,\cdots\)D.\(0,0,0,0,\cdots\)2.等比數(shù)列\(zhòng)(\{a_n\}\)中,公比\(q=2\),\(a_1=1\),則()A.\(a_2=2\)B.\(a_3=4\)C.\(a_4=8\)D.\(a_5=16\)3.數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式\(a_n=2n-1\),則()A.\(a_1=1\)B.\(a_2=3\)C.\(a_3=5\)D.\(a_4=7\)4.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(d=2\),則()A.\(a_2=3\)B.\(a_3=5\)C.\(a_4=7\)D.\(a_5=9\)5.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),\(a_3=8\),則()A.\(q=2\)B.\(q=-2\)C.\(a_2=4\)D.\(a_2=-4\)6.數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2+n\),則()A.\(a_1=2\)B.\(a_2=4\)C.\(a_3=6\)D.\(a_4=8\)7.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_5=10\),\(a_{10}=20\),則()A.\(d=2\)B.\(a_1=2\)C.\(a_2=4\)D.\(a_3=6\)8.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_3=4\),\(a_5=16\),則()A.\(q=2\)B.\(q=-2\)C.\(a_4=8\)D.\(a_4=-8\)9.數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_{n+1}=2a_n\),\(a_1=1\),則()A.\(a_2=2\)B.\(a_3=4\)C.\(a_4=8\)D.\(a_5=16\)10.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1+a_2+a_3=6\),則()A.\(a_1=1\)B.\(a_2=2\)C.\(a_3=3\)D.\(d=1\)三、判斷題(每題2分,共10題)1.數(shù)列\(zhòng)(1,2,3,4,5\)是等差數(shù)列。()2.數(shù)列\(zhòng)(2,4,8,16\)是等比數(shù)列。()3.若數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2\),則\(a_n=2n-1\)。()4.等差數(shù)列\(zhòng)(\{a_n\}\)中,若\(a_m=a_n\),則\(m=n\)。()5.等比數(shù)列\(zhòng)(\{a_n\}\)中,若\(a_m=a_n\),則\(m=n\)。()6.數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_{n+1}=a_n+1\),則\(\{a_n\}\)是等差數(shù)列。(）7.數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_{n+1}=2a_n\),則\(\{a_n\}\)是等比數(shù)列。（)8.等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n\)一定是關(guān)于\(n\)的二次函數(shù)。()9.等比數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n\)一定是關(guān)于\(n\)的指數(shù)函數(shù)。()10.若數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列,則\(\{a_{2n}\}\)也是等差數(shù)列。（）四、簡答題(每題5分,共4題)1.求等差數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式,已知\(a_1=2\),\(d=3\)。2.求等比數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式,已知\(a_1=1\),\(q=2\)。3.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=2n^2-n\),求\(a_n\)。4.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_3=5\),\(a_7=13\),求\(a_5\)。五、討論題(每題5分,共4題)1.討論等差數(shù)列與等比數(shù)列的異同點(diǎn)。2.如何利用數(shù)列的通項(xiàng)公式求數(shù)列的前\(n\)項(xiàng)和?3.數(shù)列在實(shí)際生活中有哪些應(yīng)用?4.如何判斷一個數(shù)列是等差數(shù)列還是等比數(shù)列?答案一、單項(xiàng)選擇題1.C2.B3.C4.A5.A6.A7.A8.A9.A10.A二、多項(xiàng)選擇題1.ACD2.ABCD3.ABCD4.ABCD5.ABCD6.ABCD7.ABCD8.ABCD9.ABCD10.ABCD三、判斷題1.√2.√3.√4.×5.×6.√7.√8.×9.×10.√四、簡答題1.\(a_n=a_1+(n-1)d=2+3(n-1)=3n-1\)。2.\(a_n=a_1q^{n-1}=2^{n-1}\)。3.\(n=1\)時(shí),\(a_1=S_1=1\);\(n\geq2\)時(shí),\(a_n=S_n-S_{n-1}=4n-3\),\(n=1\)也滿足,所以\(a_n=4n-3\)。4.\(a_5=\frac{a_3+a_7}{2}=\frac{5+13}{2}=9\)。五、討論題1.相同點(diǎn):都有通項(xiàng)公式等;不同點(diǎn):等差數(shù)列是后一項(xiàng)減前一項(xiàng)為定值,等比數(shù)列是后一項(xiàng)除前一項(xiàng)為定值。2.可根據(jù)通項(xiàng)公式特點(diǎn),如等差數(shù)列用公式\(S_n=\frac{n(a_1