－6x ＋5＝0的两个实根， ∴a 1＝1，a 2＝5，∴等差数列{a n }的公差为4， ∴S n ＝n ·1＋
n n －1
2
·4＝2n 2
－n .
(2)证明：当c ＝－12时，b n ＝S n n ＋c ＝2n 2
－n
n －
1
2＝2n ，
∴b n ＋1－b n ＝2(n ＋1)－2n ＝2，b 1＝2.
∴数列{b n }是以2为首项，2为公差的等差数列.
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课时跟踪检测(三十三) 数列求和
课时跟踪检测(三十三) 数 列 求 和 1．已知{a n }是首项为1的等比数列，S n 是{a n }的前n 项和，且9S 3＝S 6，则数列???? ?? 1a n 的 前5项和为( ) A.158或5 B.3116或5 C.3116 D.158 2．已知数列{a n }的前n 项和S n ＝an 2＋bn (a 、b ∈R )，且S 25＝100，则a 12＋a 14等于( ) A ．16 B ．8 C ．4 D ．不确定 3．数列112，314，518，7116，…，(2n －1)＋1 2n ，…的前n 项和S n 的值等于( ) A ．n 2＋1－1 2n B ．2n 2－n ＋1－1 2 n C ．n 2＋1－ 12 n －1 D ．n 2－n ＋1－1 2 n 4．(2019·“江南十校”联考)若数列{a n }为等比数列，且a 1＝1，q ＝2，则T n ＝1a 1a 2＋ 1 a 2a 3 ＋…＋ 1 a n a n ＋1 的结果可化为( ) A ．1－1 4n B ．1－1 2n C.2 3??? ?1－14n D.2 3? ???1－12n 5．(2019·珠海模拟)已知等差数列{a n }的前n 项和为S n ，a 5＝5，S 5＝15，则数列???? ? ?1a n a n ＋1的前100项和为( ) A.100101 B.99101 C.99100 D.101100 6．已知函数f (n )＝????? n 2(当n 为奇数时)， －n 2(当n 为偶数时)， 且a n ＝f (n )＋f (n ＋1)，则a 1＋a 2＋a 3＋…＋a 100 等于( ) A ．0 B ．100 C ．－100 D ．10 200 7．在等差数列{a n }中，S n 表示前n 项和，a 2＋a 8＝18－a 5，则S 9＝________. 8．对于数列{a n }，定义数列{a n ＋1－a n }为数列{a n }的“差数列”，若a 1＝2，{a n }的“差数列”的通项公式为2n ，则数列{a n }的前n 项和S n ＝________.
人教版高中英语必修一课时跟踪检测(一)
高中英语学习材料 madeofjingetieji 课时跟踪检测（一） Warming Up & Reading — Language Points Ⅰ.单句语法填空 1．It was in prison that he set down the story. 2．After going through the woods, you’ll find a hospital. 3．The house fell down before she was able to save her little daughter. 4．She joined an English club in order to improve her English. 5．The couple told us it was the fourth time that they had_visited (visit) the West Lake. 6．Before eating, please add some salt to the dish. 7．As far as I’m concerned (concern), it is not a good idea to go camping tonight. 8.While swimming (swim) in the river, we saw a fish jump out of the river. 9．It is no good staying up too late every day. Ⅱ.完成句子 1.He was_very_upset_about_the_fact (为此事很难过) that they couldn’t go to the beach. 2．The teacher made every effort to calm_his_student_down (使他的学生冷静下来) after the exam. 3．I got up early in_order/so_as_not_to_be_late_for_school (为了上学不迟到)． 4．The police went_through_our_luggage (检查了我们的行李) before we got on the plane. 5．A_series_of_wet_days (一连串的雨天) drove me crazy. 6．The time I spend on reading every day adds_up_to_two_hours (合计两个小时)．7．I won’t go there unless_(I_am)_invited (除非受到邀请)． 8．He treated me so badly that I couldn’t_stand_it_any_longer (不能再忍受了)． Ⅲ.阅读理解 A Dear Mr Black， I used to have a really good group of friends. Now they’re all getting into smoking and drinking. I want to find a new group of friends, but I’m shy. How can I know who are the types of people I should make friends with, and who will accept me? Yours， Mike
高中语文语文版必修四课时跟踪检测(十二)+师说+Word版含答案
课时跟踪检测（十二）师说 (时间：40分钟满分：60分) 一、文言基础专练(28分) 1．下列各句中加点的词语，解释不正确的一项是(3分)( ) A．吾从而师．之师：以……为师 B．吾未见其明．也明：明智 C．君子不齿．齿：并列 D．圣人无常．师常：经常 解析：选D D项，常：固定的。 2．下列加点词语的含义与现在的用法分析正确的一组是(3分)( ) ①古之学者 ．．受业解惑也③今之众人 ．．，其下圣人也亦远矣④小．．．必有师②师者，所以传道 学．而大遗，吾未见其明也⑤弟子不必 ．． ．．不如师，师不必贤于弟子⑥年十七，好古文A．全不相同 B．②③⑤和现在的用法相同 C．全都相同 D．①③⑥和现在的用法相同 解析：选A ①学者，古义：求学之人；今义：在学术上有一定成就的人。②传道，古义：传播道理，文中指传播儒家思想；今义：通常指传播宗教思想。③众人，古义：普通人；今义：大家。④小学，古义：在文中指对小的方面学习；今义：对儿童、少年实施初等教育的学校。⑤不必，古义：不一定；今义：用不着，不需要。⑥古文，古义：先秦两汉的文字；今义：相对于白话文的文言文。 3．从句式特征看，与“师者，所以传道受业解惑也”一句相同的一项是(3分)( ) A．道之所存，师之所存也B．句读之不知，惑之不解 C．不拘于时，学于余D．圣人无常师 解析：选A A项与例句同为判断句。B项是宾语前置；C项是被动句；D项是一般句式。 4．下列句子中，“师”字的用法不同于其他三项的一项是(3分)( ) A．于其身也，则耻师．焉 B．或师．焉，或不焉 C．爱其子，择师．而教之 D．师．道之不复，可知矣 解析：选C C项为名词，译为“老师”，其他三项为动词，意为“从师”。 5．下列加点词语含义相同的一组是(3分)( )
课时跟踪检测(三十) 数列的概念与简单表示法
课时跟踪检测(三十) 数列的概念与简单表示法 1．已知数列{a n }的前n 项和为S n ，且S n ＝2(a n －1)，则a 2等于( ) A ．4 B ．2 C ．1 D ．－2 2．按数列的排列规律猜想数列23，－45，67，－8 9，…的第10项是( ) A ．－16 17 B ．－18 19 C ．－2021 D ．－22 23 3．数列{a n }的前n 项积为n 2，那么当n ≥2时，a n ＝( ) A ．2n －1 B ．n 2 C.(n ＋1)2n 2 D.n 2 (n －1)2 4．对于数列{a n }，“a n ＋1>|a n |(n ＝1,2，…)”是“{a n }为递增数列”的( ) A ．必要不充分条件 B ．充分不必要条件 C ．必要条件 D ．既不充分也不必要条件 5．(2012·北京高考)某棵果树前n 年的总产量S n 与n 之间的关系如图所示．从目前记录的结果看，前m 年的年平均产量最高，m 的值为( ) A ．5 B ．7 C ．9 D ．11 6．(2013·江西八校联考)将石子摆成如图的梯形形状．称数列5,9,14,20，…为“梯形数”．根据图形的构成，此数列的第2 012项与5的差，即a 2 012－5＝( ) A ．2 018×2 012 B ．2 018×2 011 C ．1 009×2 012 D ．1 009×2 011
7．已知数列{a n}满足a st＝a s a t(s，t∈N*)，且a2＝2，则a8＝________. 8．(2012·潮州质检)已知数列{a n}满足a1＝1，a2＝2，且a n＝a n－1 a n－2 (n≥3)，则a2 012＝ ________. 9．已知{a n}的前n项和为S n，且满足log2(S n＋1)＝n＋1，则a n＝________. 10．数列{a n}的通项公式是a n＝n2－7n＋6. (1)这个数列的第4项是多少？ (2)150是不是这个数列的项？若是这个数列的项，它是第几项？ (3)该数列从第几项开始各项都是正数？ 11．已知数列{a n}的前n项和S n＝2n2＋2n，数列{b n}的前n项和T n＝2－b n.求数列{a n}与{b n}的通项公式． 12．(2012·东莞质检)数列{a n}中，已知a1＝2，a n＋1＝a n＋cn(n∈N*，常数c≠0)，且a1，a2，a3成等比数列． (1)求c的值； (2)求数列{a n}的通项公式． 1．(2013·珠海质检)已知数列{a n}满足a1＝1，a n＋1a n＝2n(n∈N*)，则a10＝() A．64B．32 C．16 D．8
课时跟踪检测 (三十三) 三角函数的概念
课时跟踪检测 （三十三） 三角函数的概念 层级(一) “四基”落实练 1．sin 780°的值为( ) A ．－ 3 2 B ． 32 C ．－12 D ．12 解析：选B sin 780°＝sin(2×360°＋60°)＝sin 60°＝ 32 . 2．若45°角的终边上有一点(4－a ，a ＋1)，则a ＝( ) A ．3 B ．－32 C ．1 D ．32 解析：选D ∵tan 45°＝a ＋14－a ＝1，∴a ＝32. 3．已知角α的终边经过点(－5，m )(m ≠0)，且sin α＝2 5m ，则cos α的值为( ) A ．－55 B ．－ 510 C ．－25 5 D ．±255 解析：选C 已知角α终边上一点P (－5，m )(m ≠0)，且sin α＝2 5m ＝ m 5＋m 2 ，∴m 2 ＝54 ， ∴cos α＝ －5 5＋5 4 ＝－255. 4．已知角α的终边经过点(3a －9，a ＋2)，且cos α≤0，sin α>0，则实数a 的取值范围是( ) A ．(－2,3] B ．(－2,3) C ．[－2,3) D ．[－2,3] 解析：选A 由cos α≤0，sin α>0可知，角α的终边落在第二象限内或y 轴的正半轴
上，所以有? ???? 3a －9≤0， a ＋2>0， 即－2
