在数列{an}中,奇数项成等差数列,
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an+1=2√Sn令n=1,解得a1=1平方得,an²+2an+1=4Sn当n≥2时,a(n-1)²+2a(n-1)+1=4Sn-1两式相减得,an²-a(n-1)&su
S3=a1(1+q+q2)=26/9a1=2,q=1/3bn=(an+an+1)/2=(a1qn-1+a1qn)/2=a1qn-1(1+q)/2=4(1/3)n
1、由题意,得(a1+2)/2=√(2a1)整理,得(a1-2)²=0a1-2=0a1=2(an+2)/2=√(2Sn)整理,得8Sn=(an+2)²8Sn-1=[a(n-1)+2
(1)已知,2an=2+Sn.则,2a1=a1+2,a1=2n>=2时,2an-1=2+Sn-1=2+Sn-an=2+(2an-2)-an=an则数列an为以a1=2为首项,2为公比的等比数列,则an
设等比数列的公比为p,则a2=2p,a3=2p^2,a4=2p^3由题意可得2(a3+2)=a2+a4左边=2(2p^2+2)=4(p^2+1),右边=2p+2p^3=2p(p^2+1)∴4(p^2+
a2+a4=2*(a3+2),代入第一个式子,a3=8a2+a4=20a3/q+a3*q=20q=1/2或21/2舍a1=2an=2^n
看图片:前三项2,6,10(2)由题意,2sn=[(an+2)/2]的平方,sn=an平方/8+an/2+1/2,则s(n-1)=a(n-1)平方+a(n-1)/2+1/2,两式相减得:sn-s(n-
an=2^n步骤:等比数列{an},=>an=a1*q^(n-1),(a1、q不为0)=>a2=a1q,a3=a1q^2,a4=a1q^3,2a1+a3=3a2=>2a1+a1q^2=3a1q,=>q
设等比数列{an}的公比为q,则:a2=a1q,a3=a1q2,由a3是a1,a2的等差中项,得:2a3=a1+a2,即2a1q2=a1+a1q,因为a1≠0,所以2q2-q-1=0,解得:q=−12
(1)∵a2是a1和a3-1的等差中项∴a1+(a3-1)=2a21+(a3-1)=2a2a3=2a2q=2∴an=a1*q^(n-1)=2^(n-1)(2)∵bn=(2n-1)an∴bn=(2n-1
设an=a1*q^(n-1)=2q^(n-1),因为-2a2,a3+2,28成等差,所以2(a3+2)=-2a2+28,得到2(2q^2+2)=-2*2q+28,解得q=2或-3(舍去)所以an=2*
(1)an是Sn与2的等差中项即a1=2sn=2an-2所以s(n-1)=2a(n-1)-2an=sn-s(n-1)=2a(n-1)所以an为等比数列公比为2首项为2则an=2^n而点P(bn,bn+
因:Sn是An和1的等差中项所以有:2Sn=An+1即:Sn=(An+1)/2An=Sn-S(n-1)=(An+1)/2-[A(n-1)+1]/2=[An-A(n-1)]/2An=-A(n-1)A1=
n+Sn=2an,所以1+s1=2a1=2s1即s1=a1=1且n+1+S(n+1)=2a(n+1)相减得1+a(n+1)=2a(n+1)-2ana(n+1)=2an+1a(n+1)+1=2an+2=
(a3+1)是a2,a3的等差中项2(a3+1)=a2+a3a3-a2=-2数列递减与已知好像矛盾再问:已知递增等比数列{an}满足a2a3a4=64,且(a3+1)是a2,a3的等差中项,求数列{a
设等比数列的公比为q,由已知可得,a1q-a1=2,4a1q=3a1+a1q2联立可得,a1(q-1)=2,q2-4q+3=0∴q=3a1=1或q=1(舍去)∴sn=1−3n1−3=3n−12
2(a3+2)=a2+a42a3+4=a2+a42a1q²+4=a1q+a1q³a1=2代入得:4q²+4=2q+2q³q³-2q²+q-2
An,Bn,An+1成等差A1=1.B1=2所以A2=3又Bn,An+1,Bn+1成等比所以B2=9/2所以A3=6,B3=8A4=10,B4=25/2所以,An=n(n-1)/2,Bn=(n+1)^
由题意得(an+1)/2=√(Sn×1)Sn=[(an+1)/2]²n=1时,S1=a1=[(a1+1)/2]²,整理,得(a1-1)²=0a1=1n≥2时,Sn=[(a
1Sn=2n^2-nS(n-1)=2(n-1)^2-(n-1)an=Sn-S(n-1)=2n^2-n-[2(n-1)^2-(n-1)]=4n-3an-a(n-1)=(4n-3)-[4(n-1)-3]=