(1/2)设an是等差数列,bn=1/2的an次方,已知b1+b2+b3=21/8,b1·b2·b3=1/8,求等差数列的通项an n在字母

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 00:06:10
(1/2)设an是等差数列,bn=1/2的an次方,已知b1+b2+b3=21/8,b1·b2·b3=1/8,求等差数列的通项ann在字母(1/2)设an是等差数列,bn=1/2的an次方,已知b1+

(1/2)设an是等差数列,bn=1/2的an次方,已知b1+b2+b3=21/8,b1·b2·b3=1/8,求等差数列的通项an n在字母
(1/2)设an是等差数列,bn=1/2的an次方,已知b1+b2+b3=21/8,b1·b2·b3=1/8,求等差数列的通项an n在字母

(1/2)设an是等差数列,bn=1/2的an次方,已知b1+b2+b3=21/8,b1·b2·b3=1/8,求等差数列的通项an n在字母
b1·b2·b3=1/8 即 (1/2)^(a1+a2+a3)=1/8
所以 a1+a2+a3=3
因为an为等差数列 所以3*a2=3 a2=1
设公差为d
因为b1+b2+b3=21/8
所以(1/2)^(1-d)+1/2+(1/2)^(1+d)=21/8
解得d=2
所以an的通项公式为an=2n-3

bn=(1/2)^(an)
b1b2b3=(1/2)(a1+a1+d+a1+2d)=(1/2)(3a1+3d)=(1/8)^(a1+d)=1/8
a1+d=1 a2=1
b1+b2+b3=(1/2)^(a2-d)+(1/2)^(a2)+(1/2)^(a2+d)
=(1/2)^(a2)[(1/2)^(-d)+1+(1/2)^d]
=(1/2)[(1/2)^(...

全部展开

bn=(1/2)^(an)
b1b2b3=(1/2)(a1+a1+d+a1+2d)=(1/2)(3a1+3d)=(1/8)^(a1+d)=1/8
a1+d=1 a2=1
b1+b2+b3=(1/2)^(a2-d)+(1/2)^(a2)+(1/2)^(a2+d)
=(1/2)^(a2)[(1/2)^(-d)+1+(1/2)^d]
=(1/2)[(1/2)^(-d)+1+(1/2)^d]=21/8
(1/2)^(-d)+1+(1/2)^d=21/4
(1/2)^d-17/4+(1/2)^(-d)=0
等式两边同乘以4×(1/2)^d
4×[(1/2)^d]^2-17×(1/2)^d+4=0
[(1/2)^d-4][4×(1/2)^d-1]=0
(1/2)^d=4 d=-2或(1/2)^d=1/4 d=2
d=-2时,a1=a2-d=1-(-2)=3 an=a1+(n-1)d=3+(-2)(n-1)=5-2n
d=2时,a1=a2-d=1-2=-1 an=a1+(n-1)d=-1+2(n-1)=2n-3

收起

由题意,知b1=(1/2)^a1>0,当n≥2时,bn/bn-1=(1/2)^(an-an-1)=(1/2)^d为常数,故{bn}是等比数列,设(1/2)^d=q,由b1·b2·b3=1/8得b2=1/2,所以1/2q+1/2+q/2=21/8,解得q=1/4或q=4
当q=1/4时,(1/2)^d=1/4,所以d=2 , 又b1=(1/2)^a1=2,所以a1=-1,于是,an=2n-3...

全部展开

由题意,知b1=(1/2)^a1>0,当n≥2时,bn/bn-1=(1/2)^(an-an-1)=(1/2)^d为常数,故{bn}是等比数列,设(1/2)^d=q,由b1·b2·b3=1/8得b2=1/2,所以1/2q+1/2+q/2=21/8,解得q=1/4或q=4
当q=1/4时,(1/2)^d=1/4,所以d=2 , 又b1=(1/2)^a1=2,所以a1=-1,于是,an=2n-3;
当q=4时,(1/2)^d=4,所以d=-2,又b1=(1/2)^a1=1/8,所以a1=3,于是,an=5-2n.

收起

令an的公差为d
b1*b2*b3=1/2^a1*1/2^a2*1/2^a3
=1/2^a1*1/2^(a1+d)*1/2^(a1+2d)
=2^(-3a1-3d)=1/8
-3a1-3d=-3
a1+d=1
b1+b2+b3=1/2^a1+1/2^a2+1/2^a3
=1/2^a1+1/2^(a1+d)+1/2^(a1+2d)
=1...

全部展开

令an的公差为d
b1*b2*b3=1/2^a1*1/2^a2*1/2^a3
=1/2^a1*1/2^(a1+d)*1/2^(a1+2d)
=2^(-3a1-3d)=1/8
-3a1-3d=-3
a1+d=1
b1+b2+b3=1/2^a1+1/2^a2+1/2^a3
=1/2^a1+1/2^(a1+d)+1/2^(a1+2d)
=1/2^a1+1/2^(a1+1-a1)+1/2^(a1+2-2a1)
=1/2^a1+1/2+1/2^(2-a1)=21/8
1/2^a1+1/2^(2-a1)=17/8
2^(2-a1)+2^a1=17/2
a1=-1,d=2
an=a1+(n-1)d=-1+2(n-1)=2n-3

收起

设等差数列an首项a1,公差d
b1·b2·b3=1/8 (1/2)^3(a1+d)=1/8 a1+d=1
b1+b2+b3=21/8 (1/2)^a1[1+(1/2)^d+(1/2)^2d]=21/8
解得:a1= -1 d=2 或 a1=3 d= -2
an =a1+(n-1)d=2n-3 或5-2n
故:等差数列的通项an =2n-3 或5-2n

如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗? an+1^2-a^2=bn an是等差数列 求证bn是等差数列 设{an}是等差数列,an=2n-1,{bn}是等比数列,bn=2^(n-1)求{an/bn}前n项和Sn 一道求证等差数列题目,a1=1 ,an=2a(n-1)+ 2^(n-1) 设bn= an/2^(n-1) 求证bn是等差数列 求证等差数列,a1=1 ,an=2a(n-1)+ 2^(n-1) 设bn= an/2^(n-1) 求证bn是等差数列 如何证明:已知数列{an}是等差数列,设bn=2an+3a(n+1).求证:数列{bn}也是等差数列. 已知数列{an},{bn}满足a1=2,2an=1+2an*an+1,设{bn}=an-1求数列{1n}为等差数列急!!! 设{an}是等差数列,bn=1/2^an,已知b1+b2+b3=21/8,b1*b2*b3=1/8,求等差数列的通项an? 设{an}是等差数列,bn=1/2^an,已知b1+b2+b3=21/8,b1*b2*b3=1/8,求等差数列的通项an? a1=1,an+1=2an+2^n 设bn=an/2^n-1 1证明bn是等差数列 2求an前n项和sna1=1,an+1=2an+2^n 设bn=an/2^n-1 1.证明bn是等差数列 2.求an前n项和sn 设数列{an}是等差数列,bn=(1/2)的an次方,又b1+b2+b3=21/8,b1b2b3=1/8,证明数列{bn}是等比数列 设{an}是等差数列,bn={1/2}^an,已知b1+b2+b3=21/8,b1b2b3=1/8,证明{bn}是等比数列 数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)设bn=1/1-an,证明{bn}是等差数列,并求bn和an各位哥哥姐姐们谁会啊? 设各项均为正数的数列{an}和{bn}满足:an,bn,an+1成等差数列,bn,an+1,bn+1等比数列且a1=1,b1=2,a2=3求通项an,bn 设各项均为正数的数列{an}和{bn}满足:an,bn,an+1成等差数列,bn,an+1,bn+1成等比数列,且a1=1,b1=2,a2=3,求通项an,bn 一道数学数列题设两个数列{An},{Bn}满足Bn=(A1+A2+A3+……+nAn)/(1+2+3+……+),若{Bn}为等差数列,求证{An}也是等差数列.那个,题目上是“若{Bn}为等差数列,求证{An}也是等差数列”要是“若{an}为等 在数列an中,a1=2,a2=4,an+1=3an-2an-1,设bn=log2(an+1-an)求证bn是等差数列,求数列1/bnbn+1的前n项和 一道数学题(等差数列)设各项均为正数的无穷数列{an}和{bn}满足:对任意n属于N8,都有2bn=an乘以an+1,且a^2 n+1=bn乘以bn+1求证:{根号bn}是等差数列求思路!设各项均为正数的无穷数列{a[n]}和{b[n]}