已知{an}的前n项之和Sn=n^2-4n 1,当n大于等于3

a(1)=s(1)=1-5a(1)-85,6a(1)=-84,a(1)=-14.a(n+1)=s(n+1)-s(n)=(n+1)-5a(n+1)-85-[n-5a(n)-85]=1-5a(n+1)+5

a1=5an=-3^n/2+2(n≥2)

已知等差数列an的前n项之和是Sn,则-am

99=a2+a4+a6=(a1+a3+a5)+3d=105+3dd=-2a1+a3+a5=3a1+2d+4d=3a1+6d=105a1=39an=39-2(n-1)=41-2n>0n

已知数列(an)的前n项之和为Sn,(1)Sn=-n²+2nn=1时,a1=S1=-1²+2=1n>1时,an=Sn-S(n-1)=[-n²+2n]-[-(n-1)

n=1,S1=a1=(a1-1)/3,a1=-1/2;n=2,S2=a1+a2=(a2-1)/3,a2=+1/4;an=Sn-Sn-1=（an-1）/3-（an-1-1）/3=an/3-an-1/32

an看做两个数列,其中n^2求和根据平方数列求和公式为：n(n+1)(2n+1)/6n求和根据等差数列求和公式为：(1+n)*n/2两者相加即为答案

Sn=n-5an-85(1)S（n+1）=n+1-5a（n+1）-85(2)(2)-(1)整理得6a(n+1)=1+5an即a(n+1)-1=(5/6)(an-1)又由S1=a1=1-5a1-85得a

1.n=1时,a1=S1=1²+1=2n≥2时,Sn=n²+nS(n-1)=(n-1)²+(n-1)an=Sn-S(n-1)=n²+n-(n-1)²-

Sn=(103n-3n^2)/2S1=a1=50Sn-1=[103(n-1)-3(n-1)^2]/2Sn-Sn-1=an=53-3na1a2……a17都是正数,后面的是负数设Tn=｜an｜的n项之和n

（1）证明：∵Sn=n-5an-85，n∈N*（1）∴Sn+1=（n+1）-5an+1-85（2），由（2）-（1）可得：an+1=1-5（an+1-an），即：an+1-1=56（an-1），从而{

1.证：n≥2时,2Sn²=2anSn-an=2[Sn-S(n-1)]Sn-[Sn-S(n-1)]整理,得S(n-1)-Sn=2SnS(n-1)等式两边同除以SnS(n-1)1/Sn-1/S

A(n+1)=S(n+1)-Sn=2(n+1)^2+3(n+1)+2-2n^2-3n-2=2n^2+4n+2+3n+3-2n^2-3n=4n+5An=5+4(n-1)

S7=7,S15=75,设公差是d,首项是a1则7a1+(7*6/2)d=7,15a1+(15*14/2)*d=75∴a1+3d=1且a1+7d=5∴d=1,a1=-2∴Sn=na1+n(n-1)*d

Sn=5^(n-1)+kSn-1=5^(n-2)+kan=sn-sn-1=5^(n-1)+k-(5^(n-2)+k)=4/5*5^(n-1)a1=4/5q=5Sn=(a1-an*q)/(1-q)=(4

n=1时,S1=a1=2-1=1n≥2时,Sn=2-n³S(n-1)=2-(n-1)³an=Sn-S(n-1)=2-n³-2+(n-1)³=-3n²+

S9=18(a1+a9)*9/2=18a1+a9=4a1+a1+(9-1)*d=4a1+4d=2a1=2-4da(n-4)=30a1+(n-4-1)*d=30a1+(n-5)d=302-4d+(n-5

由Sn=n^2+3n得S(n-1)=(n-1)^2+3(n-1),两式相减,考虑到Sn-S(n-1)=an得an=2n-1+3=2n+4,于是得a(n-1)=2(n-1)+4,两式相减得an-a(n-

1.n=1时,S1=a1=(a1²+a1)/2,整理,得a1²-a1=0a1(a1-1)=0a1=0(与已知不符,舍去)或a1=1S1=a1=1n≥2时,Sn=(an²+

an+Sn=41a(n+1)+S(n+1)=2a(n+1)+Sn=422-1得2a(n+1)-an=0a(n+1)=1/2anan+Sn=4an≠0a(n+1)/an=1/2数列{an}是等比数列