求数列通项公式常用的七种方法

求数列通项公式常用的七种方法1、公式法：已知或根据题目的条件能够推出数列为等差或等比数列，根据通项公式或进行求解.例1：已知是一个等差数列，且，求的通项公式.分析：设数列的公差为，则解得二、前项和法：已知数列的前项和的解析式，求.例2：已知数列的前项和，求通项.分析：当时，==而不适合上式，三、与的关系式法：已知数列的前项和与通项的关系式，求.例3：已知数列的前项和满足，其中，求.分析：①②①-②得即又不适合上式数列从第2项起是以为公比的等比数列EMBEDEquation.3注：解决这类问题的方法，用具俗话说就是“比着葫芦画瓢”，由与的关系式，类比出与的关系式，然后两式作差，最后别忘了检验是否适合用上面的方法求出的通项.四、累加法：当数列中有，即第项与第项的差是个有“规律”的数时，就可以用这种方法.例4：EMBEDEquation.3，求通项分析：┅以上各式相加得又，所以，而也适合上式，五、累乘法：它与累加法类似，当数列中有，即第项与第项的商是个有“规律”的数时，就可以用这种方法.例5：求通项分析：EMBEDEquation.DSMT4EMBEDEquation.DSMT4故而也适合上式，所以六、构造法：㈠、一次函数法：在数列中有（均为常数且），从 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 面形式上来看是关于的“一次函数”的形式，这时用下面的方法:一般化方法：设则而EMBEDEquation.DSMT4即故数列是以为公比的等比数列，借助它去求例6：已知求通项分析：EMBEDEquation.DSMT4EMBEDEquation.DSMT4数列是以为首项，为公比的等比数列EMBEDEquation.DSMT4故㈡、取倒数法：这种方法适用于EMBEDEquation.DSMT4（均为常数），两边取倒数后得到一个新的特殊(等差或等比)数列或类似于的式子.例7：已知求通项EMBEDEquation.DSMT4EMBEDEquation.DSMT4即数列是以为首项，以为公差的等差数列EMBEDEquation.DSMT4EMBEDEquation.DSMT4㈢、取对数法：一般情况下适用于（为非零常数）例8：已知求通项分析：由知EMBEDEquation.DSMT4在的两边同取常用对数得即数列是以为首项，以为公比的等比数列故EMBEDEquation.DSMT4七、“（为常数且不为，）”型的数列求通项.例9：设数列的前项和为，已知，求通项.解：两式相减得即上式两边同除以得（这一步是关键）令得（想想这步是怎么得来的）数列从第项起，是以为首项，以为公比的等比数列故又，所以不适合上式注：求（为常数且不为，）”型的数列求通项公式的方法是等式的两边同除以，得到一个“”型的数列，再用上面第六种方法里面的“一次函数法”便可求出的通式，从而求出.另外本题还可以由得到即,按照上面求的方法同理可求出,再求.您不不妨试一试.除了以上七种方法外，还有嵌套法（迭代法）、归纳猜想法等，但这七种方法是经常用的，将其总结到一块，以便于学生记忆和掌握._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_1234567908.unknown_1234567909.unknown_1234567910.unknown_1234567911.unknown_1234567912.unknown_1234567913.unknown_1234567914.unknown_1234567915.unknown_1234567916.unknown_1234567917.unknown_1234567918.unknown_1234567919.unknown_1234567920.unknown_1234567921.unknown_1234567922.unknown_1234567923.unknown_1234567924.unknown_1234567925.unknown_1234567926.unknown_1234567927.unknown_1234567928.unknown_1234567929.unknown_1234567930.unknown_1234567931.unknown_1234567932.unknown_1234567933.unknown_1234567934.unknown_1234567935.unknown_1234567936.unknown_1234567937.unknown_1234567938.unknown_1234567939.unknown_1234567940.unknown_1234567941.unknown_1234567942.unknown_1234567943.unknown_1234567944.unknown_1234567945.unknown_1234567946.unknown_1234567947.unknown_1234567948.unknown_1234567949.unknown_1234567950.unknown_1234567951.unknown_1234567952.unknown_1234567953.unknown_1234567954.unknown_1234567955.unknown_1234567956.unknown_1234567957.unknown_1234567958.unknown_1234567959.unknown_1234567960.unknown_1234567961.unknown_1234567962.unknown_1234567963.unknown_1234567964.unknown_1234567965.unknown_1234567966.unknown_1234567967.unknown_1234567968.unknown_1234567969.unknown_1234567970.unknown_1234567971.unknown_1234567972.unknown_1234567973.unknown_1234567974.unknown_1234567975.unknown_1234567976.unknown_1234567977.unknown_1234567978.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_1234568061.unknown_1234568062.unknown_1234568063.unknown_1234568064.unknown_1234568065.unknown_1234568066.unknown_1234568067.unknown_1234568068.unknown_1234568069.unknown_1234568070.unknown_1234568071.unknown_1234568072.unknown_1234568073.unknown_1234568074.unknown_1234568075.unknown_1234568076.unknown_1234568077.unknown_1234568078.unknown_1234568079.unknown_1234568080.unknown_1234568081.unknown_1234568082.unknown_1234568083.unknown_1234568084.unknown_1234568085.unknown_1234568086.unknown_1234568087.unknown_1234568088.unknown_1234568089.unknown_1234568090.unknown_1234568091.unknown_1234568092.unknown_1234568093.unknown_1234568094.unknown_1234568095.unknown_1234568096.unknown_1234568097.unknown_1234568098.unknown_1234568099.unknown_1234568100.unknown_1234568101.unknown_1234568102.unknown_1234568103.unknown_1234568104.unknown_1234568105.unknown_1234568106.unknown_1234568107.unknown_1234568108.unknown_1234568109.unknown