正项等比数列a1和a4031是函数f(x)=1 3x的极值点,则log根号6

令an的公比为q,bn的公差为da3+b5=q^2+1+4d=13,a5+b3=q^4+1+2d=21∵{an}各项为正,q>0∴d=2,q=2Sn=a1(1-q^n)/(1-q)=2^n-1bn=a

A(n+1)=2S(n)+1,A(n)=2S(n-1)+1,A(n+1)-A(n)=2[S(n)-S(n-1)]=2[A(n)],A(n+1)=3A(n)所以,数列{A(n)}是首项为1,公比为3的等

假设an公比=q其次用到对数运算定律logax-logay=loga(x/y)b(n+1)-b(n)=log2an+1-log2an=log2(an+1/an)=log2q=常数所以b(n)等差所以d

10Sn=(an)²+5an+610S(n-1)=(a(n-1))²+5a(n-1）+6两式相减,得5a(n-1)+5an=(an)²-(a(n-1))²5=a

Gn=a1^2+a^2+…+an^2=a1^2q^0+a1^2q^2+…+a1^2q^(2n-2)=a1^2(q^2n-1)/(q^2-1)Sn=a1(q^n-1)/(q-1)limGn/Sn=lim

a1*a17=a9^2=16所以a9=4又a11=16,a11=a9*q^2d^2=a11/a9=4q=2所以an=a9*q^(n-9)=4*2^(n-9)=2^(n-7)

（1）设｛an｝公比为q,则bn+1/bn=log2(an+1/an)=log2(q)为常数（2）若q＝1/4,即{bn}公差为log2(1/4)=-2所以,Sn=－n(平方)+4n,当n=2时,有最

1、设公差为d,公比为q.2、数列表达式an=3+(n-1)d;;bn=q^(n-1);Sn=(a1+an)*n/2=3n+(n-1)nd/23、列方程①q(6+d)=64;②q^2*（9+3d)=9

因为a3+a5+a7=9所以3*a5=9所以a5=3所以a5-a1=4d=3-1=2（d是公差）所以d=0.5所以an=a1+(n-1)d=1+(n-1)*0.5即an=0.5n+0.5字数不够bn过

a3=b3a1+2d=b1*q^2=a1*q^2a1+2d=a1*q^2.1a7=b5a1+6d=b1*q^4=a1*q^4a1+6d=a1*q^4.21式×3-2式2a1=3a1*q^2-a1q^4

设公比为q,则a3=a1q^2a5=a1q^4由题意得2(S5+a5)=S3+a3+S4+a4即2(a1+a2+a3+a4+a5+a5)=a1+a2+a3+a3+a1+a2+a3+a4+a4整理得4a

∵a(n+1)=（n+2)Sn/n且a(n+1)=S(n+1)-Sn∴S(n+1)-Sn=(n+2)*Sn/n∴S(n+1)=[(n+2)/n+1]Sn=(2n+2)/n*Sn∴S(n+1)/(n+1

设公比为q,数列是递增数列,q>1数列是等比数列,a1a5=a2a4=729,又a1+a5=246,a1、a5是方程x²-246x+729=0的两根.(x-3)(x-243)=0x=3或x=

1.an=Sn-S(n-1)=2n^2-3n-2(n-1)^2+3(n-1)=4n-5a1=-1b1=-a1=1a2=3b3(a2-a1)=b3(3+1)=1b3=1/4=b1q^2=q^2q=1/2

由于{an}为等差数列,故：a3=a1+2d,a7=a1+6da3+a7=2a1+8d=2+8d=10解得：d=1故：an=a1+(n-1)d=1+(n-1)=n(n属于N+)所以：a4=4由于{bn

不成等比数列∵s1,s2,.sn成等比数列则S1,S2,S3必有S1*S3=S2^2即a1*(a1+a2+a3)=(a1+a2)^2化简得a1a3=a2^2+a1a2①若a1,a2..成等比数列成立必

2¹ºS30-2¹ºS20-S20+S10=0移项后得到2¹º（S30-S20）=S20-S10也就是说,2¹º（a30

是{bn}的前7项的和S7最大吧?再问：也许吧。帮我做一下吧再答：因为{an}为正项等比数列，bn=lgan，所以{bn}为等差数列，b1=lg10=1,{bn}的前n项和为sn，sn=nb1+n(n

a1²=S-a1S=a1/(1-q)其中|q|

log2(a1a2*……*a2009)=2009a1a2*……*a2009=2^2009a1a2009=a2a2008=……=a1004a1006=(a1005)²所以a1a2*……*a20