求数列通项公式的方法教学说课例题习题

求数列的通项公式的方法1.定义法：①等差数列通项公式；②等比数列通项公式。例1．等差数列是递增数列，前n项和为，且成等比数列，．求数列的通项公式.解：设数列公差为∵成等比数列，∴，即EMBEDEquation.3∵，∴………………………………①∵∴…………②由①②得：，∴点评：利用定义法求数列通项时要注意不用错定义，设法求出首项与公差（公比）后再写出通项。练一练：已知数列试写出其一个通项公式：__________；2.公式法：已知（即）求，用作差法：。例2．已知数列的前项和满足．求数列的通项公式。解：由当时，有……，经验证也满足上式，所以点评：利用公式求解时，要注意对n分类讨论，但若能合写时一定要合并．练一练：①已知的前项和满足，求；②数列满足，求；3.作商法：已知求，用作商法：。如数列中，对所有的都有，则______；4.累加法：若求：EMBEDEquation.DSMT4EMBEDEquation.DSMT4。例3.已知数列满足，，求。解：由条件知：分别令，代入上式得个等式累加之，即所以，如已知数列满足，EMBEDEquation.DSMT4，则=________；5.累乘法：已知求，用累乘法：EMBEDEquation.DSMT4。例4.已知数列满足，，求。解：由条件知，分别令，代入上式得个等式累乘之，即又，如已知数列中，，前项和，若，求6.已知递推关系求，用构造法（构造等差、等比数列）。（1）形如、（为常数）的递推数列都可以用待定系数法转化为公比为的等比数列后，再求。①解法：把原递推公式转化为：，其中，再利用换元法转化为等比数列求解。例5.已知数列中，，，求.解：设递推公式可以转化为即.故递推公式为,令，则,且所以是以为首项，2为公比的等比数列，则,所以.②解法：该类型较类型3要复杂一些。一般地，要先在原递推公式两边同除以，得：引入辅助数列（其中），得：再应用的方法解决.。例6.已知数列中，,，求。解：在两边乘以得：令，则,应用例7解法得：所以练一练①已知，求；②已知，求；（2）形如的递推数列都可以用倒数法求通项。例7：解：取倒数：是等差数列，EMBEDEquation.3EMBEDEquation.3练一练：已知数列满足=1，，求；数列通项公式课后练习1已知数列中，满足a＝６，a+1=2(a+1)（n∈N）求数列的通项公式。2已知数列中，a＞0,且a＝３，＝＋１　　（n∈N）3已知数列中，a＝３，a＝a＋１（n∈N）求数列的通项公式4已知数列中，a＝１，a＝3a＋２，求数列的通项公式5已知数列中，a≠０，a＝，a＝　　（n∈N）　求a6设数列满足a=4，a=2，a=1若数列成等差数列，求a7设数列中，a=2，a=2a+1求通项公式a8已知数列中，a=1，2a=a+a求a_1139044873.unknown_1139044922.unknown_1139044943.unknown_1139044979.unknown_1146898564.unknown_1146914348.unknown_1146914375.unknown_1146931750.unknown_1146931751.unknown_1147016221.unknown_1147017908.unknown_1170848158.unknown_1171709445.unknown_1171709604.unknown_1172583250.unknown_1172583269.unknown_1179060316.unknown_1179060390.unknown_1179121418.unknown_1181409074.unknown_1181409130.unknown_1181409393.unknown_1204119106.unknown_1204119127.unknown_1204119128.unknown_1204119129.unknown_1204119130.unknown_1204119131.unknown_1204119409.unknown_1204119573.unknown_1204119707.unknown_1204119812.unknown_1204119837.unknown_1204120494.unknown_1204659531.unknown_1204659548.unknown_1204832439.unknown_1205263891.unknown_1205263892.unknown_1205263893.unknown_1205263922.unknown_1205263923.unknown_1205263954.unknown_1205264038.unknown_1205264090.unknown_1205264091.unknown_1205264092.unknown_1205264477.unknown_1205264725.unknown_1206038238.unknown_1206038239.unknown_1206038257.unknown_1206038267.unknown_1206038326.unknown_1206039959.unknown_1206340900.unknown_1206340924.unknown_1234567890.unknown_1234567891.unknown_1234567892.unknown_1234567893.unknown_1234567894.unknown_1234567895.unknown_1234567896.unknown_1234567897.unknown_1234567898.unknown_1234567899.unknown_1234567900.unknown_1234567901.unknown_1234567902.unknown_1234567903.unknown_1234567904.unknown_1234567905.unknown_1234567906.unknown_1234567907.unknown_1234567913.unknown_1234567914.unknown_1234567915.unknown_1234567916.unknown_1234567917.unknown_1234567918.unknown_1234567919.unknown_1234567920.unknown_1234567921.unknown_1234567929.unknown_1234567930.unknown_1234567931.unknown_1234567932.unknown_1234567933.unknown_1234567934.unknown_1234567935.unknown_1234567936.unknown_1234567938.unknown_1234567939.unknown_1234567940.unknown_1234567945.unknown_1234567946.unknown_1234567947.unknown_1234567948.unknown_1234567949.unknown_1234567950.unknown_1234567951.unknown_1234567955.unknown_1234567956.unknown_1234567979.unknown_1234567980.unknown_1234567981.unknown_1234567982.unknown_1234567983.unknown_1234567984.unknown_1234567985.unknown_1234567986.unknown_1234567987.unknown_1234567988.unknown_1234567989.unknown_1234567990.unknown_1234567991.unknown_1234567992.unknown_1234567993.unknown_1234567994.unknown_1234567995.unknown_1234567996.unknown_1234567997.unknown_1234567998.unknown_1234567999.unknown_1234568000.unknown_1234568001.unknown_1234568002.unknown_1234568003.unknown_1234568004.unknown_1234568005.unknown_1234568006.unknown_1234568007.unknown_1234568008.unknown_1234568009.unknown_1234568010.unknown_1234568011.unknown_1234568012.unknown_1234568013.unknown_1234568014.unknown_1234568015.unknown_1234568016.unknown_1234568017.unknown_1234568018.unknown_1234568019.unknown_1234568020.unknown_1234568021.unknown_1234568022.unknown_1234568023.unknown_1234568024.unknown_1234568025.unknown_1234568026.unknown_1234568027.unknown_1234568028.unknown_1234568029.unknown_1234568030.unknown_1234568031.unknown_1234568032.unknown_1234568033.unknown_1234568034.unknown_1234568035.unknown_1234568036.unknown_1234568037.unknown_1234568038.unknown_1234568039.unknown_1234568040.unknown_1234568041.unknown_1234568042.unknown_1234568043.unknown_1234568044.unknown_1234568045.unknown_1234568046.unknown_1234568047.unknown_1234568048.unknown_1234568049.unknown_1234568050.unknown_1234568051.unknown_1234568052.unknown_1234568053.unknown_1234568054.unknown_1234568055.unknown_1234568056.unknown_1234568057.unknown_1234568058.unknown_1234568059.unknown_1234568060.unknown_1234568449.unknown_1234568450.unknown_1234568451.unknown_1234568452.unknown_1234568453.unknown_1234568454.unknown