已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/2
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/19 22:47:39
已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/2
1.求数列{an}的通项公式
2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求实数t的值以及数列{bn}的通项公式
1.求数列{an}的通项公式
2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求实数t的值以及数列{bn}的通项公式
an=a1.q^(n-1)
a(n+1)=a1+a2+...+a(n-1)+(5/2)an+1/2
n=1,
a2=(5/2)a1+1/2
a1q =(5/2)a1+1/2 (1)
n=2,
a3=a1+(5/2)a2+1/2
a1q^2=a1+(5/2)a1q+1/2 (2)
(2)-(1)
q(q-1) =-(3/2) +(5/2)q
2q^2-7q+3=0
(2q-1)(q-3)=0
q=3 (q>1)
from (1)
a1q =(5/2)a1+1/2
3a1=(5/2)a1+1/2
a1=1
ie
an= 3^(n-1)
(2)
bn=b1+(n-1)d
bn=(1/n)[ log(a1)+log(a2)+...+log(an)+log(t) ]
=(1/n)[ n(n-1)/2 +log(t) ]
n=1,
b1 =log(t) (3)
n=2,
b2=(1/2)[ 1 +log(t) ]
b1+d =(1/2)[ 1 +log(t) ] (4)
(4)-(3)
d= (1/2)[ 1 -log(t) ]
n=3,
b3=(1/3)[ 3 +log(t) ]
b1+2d=(1/3)[ 3 +log(t) ] (5)
(5)-(4)
d = 1/2 -(1/6)log(t)
(1/2)[ 1 -log(t) ] =1/2 -(1/6)log(t)
t=1
d=1/2
b1=0
bn= (n-1)/2
a(n+1)=a1+a2+...+a(n-1)+(5/2)an+1/2
n=1,
a2=(5/2)a1+1/2
a1q =(5/2)a1+1/2 (1)
n=2,
a3=a1+(5/2)a2+1/2
a1q^2=a1+(5/2)a1q+1/2 (2)
(2)-(1)
q(q-1) =-(3/2) +(5/2)q
2q^2-7q+3=0
(2q-1)(q-3)=0
q=3 (q>1)
from (1)
a1q =(5/2)a1+1/2
3a1=(5/2)a1+1/2
a1=1
ie
an= 3^(n-1)
(2)
bn=b1+(n-1)d
bn=(1/n)[ log(a1)+log(a2)+...+log(an)+log(t) ]
=(1/n)[ n(n-1)/2 +log(t) ]
n=1,
b1 =log(t) (3)
n=2,
b2=(1/2)[ 1 +log(t) ]
b1+d =(1/2)[ 1 +log(t) ] (4)
(4)-(3)
d= (1/2)[ 1 -log(t) ]
n=3,
b3=(1/3)[ 3 +log(t) ]
b1+2d=(1/3)[ 3 +log(t) ] (5)
(5)-(4)
d = 1/2 -(1/6)log(t)
(1/2)[ 1 -log(t) ] =1/2 -(1/6)log(t)
t=1
d=1/2
b1=0
bn= (n-1)/2
已知数列{an},若a1,a2-a1,a3-a2,a4-a3,an-an-1是公比为2的等比数列,则{an}的前n项和s
已知数列an为公比大于1的等比数列 有an+1=a1+a2+、、、+an-1+5/2an+1/2 求数列an的通项公式
在数列{an}中,已知对任意正整数n,有a1+a2+...+an=2的n次方-1,那么a1的平方+a2的平方+...+a
已知数列{an}满足a1=a2=1,an+2=an+1+an,n∈N*则使an>100的n的最小值是
等比数列的计算!在等比数列an中,已知对任意正整数n,有Sn=2^n-1,则a1^2+a2^2+.+an^2等于什么
问高二数列题1.等比数列中,已知对任意正整数n,a1+a2+a3+……+an=2的n次方-1,则a1²+a2&
已知等比数列{an}的通项公式为an=3^(n-1),设数列{bn}满足对任意自然数n都有b1/a1+b2/a2+b3/
等比数列an的公比为q,则a1大于0而且q大于1是对于任意自然数n,都有an+1大于an的__________条件
已知数列{an}满足条件:a1=5,an=a1+a2+...a(n-1) n大于等于2,求数列{an}的通项公式
在数列{an}中,已知对任意正整数n,有a1+a2+...+an=(2^n)-1那么a1^2+a2^2+..,+an^2
已知数列An为等比数列,公比q=-1/2,lim(a1+a2+a3+.an/a2+a4+.+a2n)的值
已知a1+a2+a3+.+an=n-an 求证an-1为等比数列 令bn=(2-n)(an-1) 如果对任意n