Question

高一数学选择题1～8

Answer 1

1
a7+a9=2a8=16
a4=1
a1=-17/4
d=7/4
a12=a1+11d
=15
2
第n个图
1个完整正六方形由6个白块1个黑块
每两个正六方形之间需要减去两个白块
白块=6*n-2(n-1)
=4n+2
3
S6=36
Sn=324
Sn-6=144
S6=(a1+a6)*6/2=36

a1+a6=12

Sn-S(n-6)=[a(n-5)+an]*6/2=324-144=180

a(n-5)+an=60
a6+a(n-5)=a1+an

a1+an=(12+60)/2=36

Sn=(a1+an)*n/2=324，故n=324*2/36=18

具体:
http://zhidao.baidu.com/link?url=Kg8b6m5OkTq7-oNXjDZt9ydDGCVGCZt-DaYEstFiP2tHsFVy1w1REYvlZkwFWns6dLHBy1F_X9dZzvJD_mwHy_
4
∵S4=S8，
则a5+a6+a7+a8=0
即a6+a7=0
∵a1＞0
∴d＜0，a6＞0，a7＜0
Sn取最大值时n=6

具体:http://www.mofangge.com/html/qDetail/02/g0/201312/tfb3g002401534.html
5
an=log2 (n+1)/(n+2)
=log2 (n+1)-log2 (n+2)
Sn=log2 2-log2 3+log2 3-log2 4+……+log2 (n+1)-log2 (n+2)
=1-log2 (n+2)<-5
n>62
6
S奇/S偶=27/32
S12=354
S偶-S奇=6d
d=5
S奇=162
S偶=192
7
x²-2x+m=0和x²-2x+m=0的四个解为x1,x2,x3,x4
x1+x2+x3+x4=4
x1+x2=2
x3+x4=2
x1x2=m
x3x4=n
x1x2是首尾两项或中间两项
不设设数列是x1,x3,x4,x2
x1=1/4,则x2=2-x1=7/4
m=x1x2=7/16
d=(x2-x1)/3=1/2
所以x3=1/4+1/2=3/4
x4=5/4
n=x3x4=15/16
|m-n|=|7/16-15/16|=1/2
具体
http://zhidao.baidu.com/link?url=bgr-_mF8nRsR6sJZ1hM7oZh1-McaZ9S9VixutaH83HqGbBoJpkL8EIQVSlJQ7QHwmiCb1V_FRHkJK5JmU0CSXq
8
a1=0
a2=-√3
a3=√3
a4=0
……
T=3
a20=2

Answer 2

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