已知等差数列首项a1,公差为d,在前四项去掉一项,其余三项成等比,则a1除以d=

根据等差数列前n项和公式,Sn=n*a1+d*n(n-1)/2=na+n(n-1)S1=a1=a,S2=2a+2,S4=4a+12S1,S2,S4成等比数列,则S2²=S1*S4,即(2a+

1.因为等差数列AN的公差d不等于0,a1=2,s9=36,所以36=9*2+1/2*9*8d所以d=1/2所以a3=3,a9=6,由a3,a9,am成等比数列则a9的平方=a3*am,的am=12又

S5+S6+15=05+S6+15=0S6=-20S5=a1+a2+a3+a4+a5=a1+(a1+d)+(a1+2d)+(a1+3d)+(a1+4d)=5*a1+10*d=5a1+2d=1d=(1-

S5=5a+(1+2+3+4）d=5a+10d=S(式1）S2=2a+dS6=6a+15dS2*S6+15=(2a+d)(6a+15d)+15=0即(2a+d)(2a+5d)+5=0(10a+5d)(

Sn=d/2n^2+(a1-d/2)n,(1).Sn+Sm=d/2(n^2+m^2)+(a1-d/2)(n+m)>=d/2(n^2+m^2+2nm)/2+(a1-d/2)(n+m)=d/22p^2+(

an=nSn=(n+1)*n/2bn=2/[(n+1)*n)]=2[1/n-1/(n+1)]b1+b2+...+bn=2{(1-1/2)+(1/2-1/3)+...+[1/n-1/(n+1)]}=2-

因为等差数列{an}的首项a1=1所以a2=a1+d=1+d,a5=a1+4d=1+4d,a14=a1+13d=1+13d因为{bn}为等比数列所以(b3)^2=b2*b4又a2=b2,a5=b3,a

由题意可得an=a1+（n-1）d=1+23（n-1）=2n+13，∵bn=（-1）n-1anan+1，∴当n为偶数时，Sn=b1+b2+…+bn=a1a2-a2a3+a3a4-a4a5+…+an-1

a2=a1+d,a3=a1+2d.,a6=a1+5d,...,a10=a1+9d,若a1,a3,a6成等比数列,则a3^2=a1*a6,(a1+2d)^2=a1*(a1+5d),得到a1=4d.则(a

（1）∵等差数列{an}中a1=1，公差d=1∴Sn＝na1+n(n−1)2d＝n2+n2∴bn＝2n2+n…（4分）（2）∵bn＝2n2+n＝2n(n+1)…（6分）∴b1+b2+b3+…+bn＝2

因为a1＋a5=a2+a4＝4,所以：a2a4=3a2+a4=4解方程组：a2=1a4=3或者a2=3a4=1a4-a2=2d=2,或者a4-a2=-2d=1,或者d=-1

等差数列{An}的首项为a1,公差为dAn=a1+（n-1）dBn=3[a1+（n-1）d]+4Bn=3a1+3（n-1）d+4B(n-1)=3a1+3（n-1-1）d+4=3a1+3（n-2）d+4

等差数列拿掉有限项后的公差不变,还是d拿掉m项后,原数列的第m+1项作为新数列的第一项.而原数列的第n+1项=a1+m*d（an=a1+(n-1)*d,这里n取m+1）所以首项am+1=a1+md

3a1+3*2/2d+5a1+5*4/2d=503a1+3d+5a1+10d=508a1+13d=50a4^2=a1a13(a1+3d)^2=a1(a1+12d)a1^2+6a1d+9d^2=a1^2

(a)a3=a1+2d,a7=a1+6da3^2=a1*a7(a1+2d)^2=a1(a1+6d)a1=2da1+a3+a7=3a1+8d=6d+8d=14d=70d=5a1=2d=10(b)an=a

（1）a1a3=a1+2da7=a1+6d已知a1,a3和a7为一等比数列中的连续三项所以a3^2=a1*a7即a1^2+4a1d+4d^2=a1^2+6a1d4d^2=2a1d公差d不等於0所以a1

(1)因为等差数列{an}的首项a1=1所以a2=a1+d=1+d,a5=a1+4d=1+4d,a14=a1+13d=1+13d因为{bn}为等比数列所以(b3)^2=b2*b4又a2=b2,a5=b

第一题：因为S5=5,S5S6+15=0.所以S6=-3a6=S6-S5=-8又因为S6=6(a1+a6)/2=-3所以a1+a6=-1a1=7第二题等差数列前n项和公式得：S5=5*a1+10*dS

2=a2=(1+d)、b3=a5=(1+4d)、b4=a14=(1+13d)；由b3:b2=b4:b3得b3*b3=b2*b4,即(1+4d)*(1+4d)=(1+d)*(1+13d),解得d=2；a

A2=1+d=B2A5=1+4d=B3A14=1+13d=B4(B3)^2=B2×B4(1+4d)^2=(1+d)(1+13d)d^2=2dd>0d=2An=1+2(n-1)=2n-1B2=3B3=9