已知数列 的前 项和为 , .(Ⅰ)求数列 的通项公式;(Ⅱ)设
已知数列的前项和为,.(Ⅰ)求数列的通项公式;(Ⅱ)设,求数列的前项和....
已知数列 的前 项和为 , .(Ⅰ)求数列 的通项公式;(Ⅱ)设 ,求数列 的前 项和 .
展开
手机用户32542
2015-01-17
·
TA获得超过240个赞
知道答主
回答量:114
采纳率:100%
帮助的人:113万
关注
已知数列 ![](https://iknow-pic.cdn.bcebos.com/4a36acaf2edda3cca3671b9302e93901203f9286?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的前 ![](https://iknow-pic.cdn.bcebos.com/2e2eb9389b504fc239dc13b6e6dde71191ef6d86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 项和为 ![](https://iknow-pic.cdn.bcebos.com/50da81cb39dbb6fd10e846950a24ab18962b37d5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) , ![](https://iknow-pic.cdn.bcebos.com/d1a20cf431adcbefacb7ddb5afaf2edda2cc9f86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . (Ⅰ)求数列 ![](https://iknow-pic.cdn.bcebos.com/4a36acaf2edda3cca3671b9302e93901203f9286?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的通项公式; (Ⅱ)设 ![](https://iknow-pic.cdn.bcebos.com/34fae6cd7b899e51433d99a741a7d933c9950dd5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,求数列 ![](https://iknow-pic.cdn.bcebos.com/4afbfbedab64034f247e61b5acc379310b551dd5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的前 ![](https://iknow-pic.cdn.bcebos.com/2e2eb9389b504fc239dc13b6e6dde71191ef6d86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 项和 ![](https://iknow-pic.cdn.bcebos.com/b8389b504fc2d562688b735ee41190ef77c66c86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . |
(Ⅰ) ![](https://iknow-pic.cdn.bcebos.com/37d12f2eb9389b50a47c43e18635e5dde6116e86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ;(Ⅱ) ![](https://iknow-pic.cdn.bcebos.com/43a7d933c895d143ffc5479070f082025baf07d5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . |
试题分析:(Ⅰ)由 ![](https://iknow-pic.cdn.bcebos.com/8c1001e93901213f5cb0ed6f57e736d12e2e9586?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,求数列 ![](https://iknow-pic.cdn.bcebos.com/d01373f082025aaff381dd78f8edab64024f1ad5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的通项公式,可利用 ![](https://iknow-pic.cdn.bcebos.com/7aec54e736d12f2e50860dd34cc2d56284356886?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 来求,注意需讨论 ![](https://iknow-pic.cdn.bcebos.com/b219ebc4b74543a9e7a8597f1d178a82b80114d5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 时的情况,本题由 ![](https://iknow-pic.cdn.bcebos.com/7aec54e736d12f2e50860dd34cc2d56284356886?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,得到数列 ![](https://iknow-pic.cdn.bcebos.com/d01373f082025aaff381dd78f8edab64024f1ad5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的递推式,从而得数列 ![](https://iknow-pic.cdn.bcebos.com/d01373f082025aaff381dd78f8edab64024f1ad5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 为等比数列,利用等比数列的通项公式可得, ![](https://iknow-pic.cdn.bcebos.com/37d12f2eb9389b50a47c43e18635e5dde6116e86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ;(Ⅱ)求数列 ![](https://iknow-pic.cdn.bcebos.com/4afbfbedab64034f247e61b5acc379310b551dd5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的前 ![](https://iknow-pic.cdn.bcebos.com/2e2eb9389b504fc239dc13b6e6dde71191ef6d86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 项和 ![](https://iknow-pic.cdn.bcebos.com/b8389b504fc2d562688b735ee41190ef77c66c86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,需求出数列 ![](https://iknow-pic.cdn.bcebos.com/4afbfbedab64034f247e61b5acc379310b551dd5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的通项公式, ![](https://iknow-pic.cdn.bcebos.com/aec379310a55b319894a21c640a98226cefc17d5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,这是一个等比数列与一个等差数列对应项积所组成的数列,故可用错位相减法来求. 试题解析:(Ⅰ)当 ![](https://iknow-pic.cdn.bcebos.com/b219ebc4b74543a9e7a8597f1d178a82b80114d5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 时, ![](https://iknow-pic.cdn.bcebos.com/42a98226cffc1e17e20c2f824990f603728de9d6?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) , 1分 当 ![](https://iknow-pic.cdn.bcebos.com/8b82b9014a90f6031f033ff43a12b31bb151edd6?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 时, ![](https://iknow-pic.cdn.bcebos.com/4b90f603738da977579c2598b351f8198718e3d6?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 3分 即: ![](https://iknow-pic.cdn.bcebos.com/91ef76c6a7efce1b69a86b79ac51f3deb58f6586?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) , ![](https://iknow-pic.cdn.bcebos.com/77c6a7efce1b9d16084439d2f0deb48f8d546486?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 数列 ![](https://iknow-pic.cdn.bcebos.com/9c16fdfaaf51f3de4c311ad797eef01f3b297986?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 为以2为公比的等比数列 5分 ![](https://iknow-pic.cdn.bcebos.com/fcfaaf51f3deb48f75ea026df31f3a292cf57886?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 7分 (Ⅱ) ![](https://iknow-pic.cdn.bcebos.com/f2deb48f8c5494ee0ba1acaa2ef5e0fe98257e86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 9分 ![](https://iknow-pic.cdn.bcebos.com/b58f8c5494eef01fc697bb76e3fe9925bd317d86?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 11分 两式相减,得 ![](https://iknow-pic.cdn.bcebos.com/f11f3a292df5e0fe669b2ab25f6034a85fdf7286?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 13分 ![](https://iknow-pic.cdn.bcebos.com/902397dda144ad3488452bc8d3a20cf430ad8583?x-bce-process=image/quality,q_85) 14分 |
收起
为你推荐: