三明高三数列题库及答案

三明高三数列题库及答案

一、单项选择题(每题2分,共10题)1.已知数列\(\{a_n\}\)满足\(a_1=1\),\(a_{n+1}=2a_n+1\),则\(a_3\)的值为（）A.3B.5C.7D.92.等差数列\(\{a_n\}\)中,\(a_2=3\),\(a_5=9\),则公差\(d\)为()A.1B.2C.3D.43.等比数列\(\{a_n\}\)中,\(a_1=2\),\(a_3=8\),则公比\(q\)为()A.2B.-2C.2或-2D.44.数列\(\{a_n\}\)的前\(n\)项和\(S_n=n^2\),则\(a_5\)的值为()A.9B.10C.11D.125.已知数列\(\{a_n\}\)满足\(a_n=\frac{n}{n+1}\),则\(a_{10}\)的值为()A.\(\frac{10}{11}\)B.\(\frac{11}{12}\)C.\(\frac{9}{10}\)D.\(\frac{12}{13}\)6.等差数列\(\{a_n\}\)的前\(n\)项和\(S_n=2n^2+n\),则\(a_1\)的值为()A.3B.2C.1D.07.等比数列\(\{a_n\}\)中,\(a_1=1\),\(a_4=8\),则\(a_2\)的值为()A.2B.-2C.4D.-48.数列\(\{a_n\}\)满足\(a_{n+1}=a_n+2\),\(a_1=1\),则\(a_{10}\)的值为()A.19B.20C.21D.229.已知等差数列\(\{a_n\}\)中,\(a_3+a_7=10\),则\(a_5\)的值为()A.5B.6C.7D.810.等比数列\(\{a_n\}\)中,\(a_2=2\),\(a_5=16\),则\(a_3\)的值为()A.4B.8C.-4D.-8二、多项选择题(每题2分,共10题)1.下列数列中是等差数列的有(）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.等比数列\(\{a_n\}\)中,公比\(q=2\),\(a_1=1\),则()A.\(a_2=2\)B.\(a_3=4\)C.\(a_4=8\)D.\(a_5=16\)3.数列\(\{a_n\}\)的通项公式\(a_n=2n-1\),则()A.\(a_1=1\)B.\(a_2=3\)C.\(a_3=5\)D.\(a_4=7\)4.等差数列\(\{a_n\}\)中,\(a_1=1\),\(d=2\),则()A.\(a_2=3\)B.\(a_3=5\)C.\(a_4=7\)D.\(a_5=9\)5.等比数列\(\{a_n\}\)中,\(a_1=2\),\(a_3=8\),则()A.\(q=2\)B.\(q=-2\)C.\(a_2=4\)D.\(a_2=-4\)6.数列\(\{a_n\}\)的前\(n\)项和\(S_n=n^2+n\),则()A.\(a_1=2\)B.\(a_2=4\)C.\(a_3=6\)D.\(a_4=8\)7.等差数列\(\{a_n\}\)中,\(a_5=10\),\(a_{10}=20\),则()A.\(d=2\)B.\(a_1=2\)C.\(a_2=4\)D.\(a_3=6\)8.等比数列\(\{a_n\}\)中,\(a_3=4\),\(a_5=16\),则()A.\(q=2\)B.\(q=-2\)C.\(a_4=8\)D.\(a_4=-8\)9.数列\(\{a_n\}\)满足\(a_{n+1}=2a_n\),\(a_1=1\),则()A.\(a_2=2\)B.\(a_3=4\)C.\(a_4=8\)D.\(a_5=16\)10.等差数列\(\{a_n\}\)中,\(a_1+a_2+a_3=6\),则()A.\(a_1=1\)B.\(a_2=2\)C.\(a_3=3\)D.\(d=1\)三、判断题(每题2分,共10题)1.数列\(1,2,3,4,5\)是等差数列。()2.数列\(2,4,8,16\)是等比数列。()3.若数列\(\{a_n\}\)的前\(n\)项和\(S_n=n^2\),则\(a_n=2n-1\)。()4.等差数列\(\{a_n\}\)中,若\(a_m=a_n\),则\(m=n\)。()5.等比数列\(\{a_n\}\)中,若\(a_m=a_n\),则\(m=n\)。()6.数列\(\{a_n\}\)满足\(a_{n+1}=a_n+1\),则\(\{a_n\}\)是等差数列。(）7.数列\(\{a_n\}\)满足\(a_{n+1}=2a_n\),则\(\{a_n\}\)是等比数列。（)8.等差数列\(\{a_n\}\)的前\(n\)项和\(S_n\)一定是关于\(n\)的二次函数。()9.等比数列\(\{a_n\}\)的前\(n\)项和\(S_n\)一定是关于\(n\)的指数函数。()10.若数列\(\{a_n\}\)是等差数列,则\(\{a_{2n}\}\)也是等差数列。（）四、简答题(每题5分,共4题)1.求等差数列\(\{a_n\}\)的通项公式,已知\(a_1=2\),\(d=3\)。2.求等比数列\(\{a_n\}\)的通项公式,已知\(a_1=1\),\(q=2\)。3.已知数列\(\{a_n\}\)的前\(n\)项和\(S_n=2n^2-n\),求\(a_n\)。4.等差数列\(\{a_n\}\)中,\(a_3=5\),\(a_7=13\),求\(a_5\)。五、讨论题(每题5分,共4题)1.讨论等差数列与等比数列的异同点。2.如何利用数列的通项公式求数列的前\(n\)项和?3.数列在实际生活中有哪些应用?4.如何判断一个数列是等差数列还是等比数列?答案一、单项选择题1.C2.B3.C4.A5.A6.A7.A8.A9.A10.A二、多项选择题1.ACD2.ABCD3.ABCD4.ABCD5.ABCD6.ABCD7.ABCD8.ABCD9.ABCD10.ABCD三、判断题1.√2.√3.√4.×5.×6.√7.√8.×9.×10.√四、简答题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.\(n=1\)时,\(a_1=S_1=1\);\(n\geq2\)时,\(a_n=S_n-S_{n-1}=4n-3\),\(n=1\)也满足,所以\(a_n=4n-3\)。4.\(a_5=\frac{a_3+a_7}{2}=\frac{5+13}{2}=9\)。五、讨论题1.相同点:都有通项公式等;不同点:等差数列是后一项减前一项为定值,等比数列是后一项除前一项为定值。2.可根据通项公式特点,如等差数列用公式\(S_n=\frac{n(a_1