已知数列{an}为等差数列,且满足an 1=an²-an 1
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已知数列{log2(an-1)}为等差数列,且a1=3,a2=5可以得到该等差数列的公差d:d=log2(a2-1)-log2(a1-1)=log2(5-1)-log2(3-1)=log2(4)-lo
1+Sn=2anSn=2an-1n>=2则S(n-1)=2a(n-1)-1相减an=2an-2a(n-1)an=2a(n-1)所以n>=2时是等比q=2a1=S1所以1+a1=2a1a1=1所以an=
①设公差为d,公比为q∵数列{an+bn}的前三项依次为3,7,13∴a1+b1=3a2+b2=7a3+b3=13又a1=1∴b1=2d=2q=2∴an=2n-1,bn=2n②∵an=2n-1,bn=
(1)设bn=log2(an+1),则{bn}为等差数列,又a1=1,a3=7,所以b1=log2(1+1)=1,b2=log(7+1)=3,所以公差d=1.所以bn=b1+(n-1)d=1+(n-1
sn=an^2+bns(n-1)=a(n-1)^2+b(n-1)两式作差,由:sn-s(n-1)=an可证.
a1*p=a2a1*p^3=a4,a1*p-a1=a1*p^3-a1*Pp-1=p^(p^2-1);(p-1)(p*(p+1)-1)=0,p=1,或p^2+p-1=0,p=(-1+√5)/2,p=(-
a1,a2,a4成等差数列2a2=a1+a4即2a1*q=a1+a1q^3a1不为0所以:2q=1+q^3q^3-2q+1=0q^3-q^2+q^2-2q+1=0q^2*(q-1)+(q-1)^2=0
a1,a2,a4成等差数列所以2a2=a1+a4{an}是等比数列a2=a1qa4=a1q^3所以2×a1q=a1+a1q^3即:q^3-2q+1=0(q-1)(q^2+q-1)=0q=1或q=(-1
设a为首相,d为工差,Ap+Aq=2a+(p+q-2)d=2a+(m+n-2)=Am+An
1.bn/b(n-1)=3[an-a(n-1)]=q所以an-a(n-1)=log(3)q2.a2=13a8=1d=-2an=17-2n3.n8Tn=-[a1+.an]+2[a1+.+a8=n^2-1
1.设首项为a,公差为da3=a+2d=-6a6=a+5d=0解得:a=-10d=2an=-10+2(n-1)=-10+2n-2=2n-122.b1=-8b2=a1+a2+a3=(2-12)+(2*2
设公差为d,a1=a2-d,a3=a2+d,则原等式变为,a2-d+a2+a2+d=15消去d,3a2=15a2=5
因为a(k1),a(k2),…,a(kn)恰为等比数列,又k1=1,k2=5,k3=17所以a5的平方=a1乘以a17又因为数列{an}为等差数列且公差d≠0所以a5=a1+4da17=a1+16d所
设数列log2(an-1)公差为dd=long2(an-1)-log2(a(n-1)-1)=log2[(an-1)/(a(n-1)-1]所以(an-1)/(a(n-1)-1)=2^d而由a1=3a2=
Sn=n(an+1)/2S(n+1)=(n+1)[a(n+1)+1]/2用下式减上式a(n+1)=[(n+1)a(n+1)-nan+1]/2即2a(n+1)=[(n+1)a(n+1)-nan+1]即(
令bn=1/(an+1),b3=1/3,b7=1/2,b7-b3=1/6=4d,d=1/24,b1=1/4bn=1/4+(n-1)/24an=(19-n)/(5+n)再问:bn转化为an的过程是什么?
设an=a1+(n-1)d,bn=an+a(n-1)=a1+(n-1)d+a1+nd=2a1+(2n-1)dbn为首项为2a1-d,公差为2d的等差数列
设an=a1+(n-1)d=10+(n-1)dSn=na1+(n-1)nd/2=10n+(n-1)nd/2S12=120+66d=-125那么d就算出来了d=-245/66所以an=10+(n-1)(
Sn、an、1成等差,则2an=Sn+1(n=1时,得a1=1),当n≥2时,有2a(n-1)=S(n-1)+1,则2an-2a(n-1)=an,即an/[a(n-1)]=2=常数,所以{an}是等比