首项为1,公差不为零,S1,S2,S3成等比数列

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

a1=a2-d,a5=a2+3d所以a2a2=（a2-d）（a2+3d）得2da2=3dd即a2=3d/2所以a1=a2-d=1d/2=1得出d=2公差=2,首项=1,后面你会的即a10=19故S10

设该等差数列首项a1,公差d则S1=a1S2=2a1+dS4=4a1+6d要成等比(2a1+d)^2=a1(4a1+6d)即4a1^2+4a1d+d^2=4a1^2+6a1d即d=2a1所以S1=a1

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设公差为d则a3=a1+2d=1+2da9=a1+8d=1+8d因为a1,a3,a9成等比数列所以a3²=a1*a9=a9∴(1+2d)²=1+8d∴d=0或者d=1又∵d≠0,∴

设公差为d（d≠0），由题意a32=a2•a6，即（a1+2d）2=（a1+d）（a1+5d），解得d=-2a1，故a1+a3+a5a2+a4+a6=3a1+6d3a1+9d=−9a1−15a1=35

S1=a1S2=a1+a2=2a1+dS4=a1+a2+a3+a4=4a1+6d因为成等比数列,所以S2的平房=S1*S4（2a1+d)的平房=a1(4a1+6d)因为d不得0解得d=2a1所以S2=

S1=a1S2=2a1+dS4=4a1+6d所以（2a1+d）²=a1（4a1+6d）解得2a1=dS1=a1S2=4a1S4=16a1数列S1,S2,S4的公比是4

(1)a3=a1+2d、a6=a1+5d.(a1+2d)^2=a1(a1+5d)a1^2+4a1d+4d^2=a1^2+5a1d4a1d+4d^2=5a1d因为d0,所以4a1+4d=5a1a1=4d

（1）设等差数列{an}的公差为d（d≠0），由a1，a3，a13成等比数列，得a32=a1•a13，即（1+2d）2=1+12d得d=2或d=0（舍去）．故d=2，所以an=2n-1（2）∵bn＝2

设公差为d,则a(n)=4+(n-1)da(1)=4,a(7)=4+6d,a(10)=4+9da(1)、a(7)、a(10)成等比,则a(7)^2=a(1)*a(10)(4+6d)^2=4*(4+9d

S1,S2,S3是等比数列,设公比为qS2/S1=qS3/S2=q又Sn为等差数列的和,设公差为dSn=a1n+n(n-1)d/2则S1=a1S2=2a1+dS3=3a1+3dS2/S1=(2a1+d

设该等差数列是首项为a1,公差为dS3=3a1+3(3-1)*d/2=3a1+3dS2=2a1+2(2-1)*d/2=2a1+dS4=4a1+4(4-1)*d/2=4a1+6d又:S3²=9

a1a2a3成等比数列a2^2=a1a3=a3(a1+d)^2=a1+2da1^2+2a1d+d^2=a1+2d1+2d+d^2=1+2dd^2=0d=0公差不为零的等差数列错题

s1=a1s2=2a1+ds4=4a1+6d因为s1,s2,s4成等比数列所以(s2)²=s1×s4(2a1+d)²=a1(4a1+6d)4a1²+4a1d+d²

数列{an}是公差不为0的等差数列，设公差为d，S1，S2，S4成等比数列，则S22=S1•S4，∴（ 2a1+d）2=a1•（4a1+6d），化简可得d=2a1∴a3a1=a1+2da1=

(1)a2²+a3²=a4²+a5²a2²-a5²=a4²-a3²(a2+a5)*(a2-a5)=(a4+a3)*(a4

（1）设数列{an}的公差为d，由题意，得S22=S1•S4所以（2a1+d）2=a1（4a1+6d）因为d≠0所以d=2a1，故a2a1=3；（2）因为a5=9，d=2a1，a5=a1+8a1=9a

Sk=(a1+ak)*k/2=[2a1+(k-1)d]*k/2=(2+k)k所以1/Sk=[(1/k)-1/(2+k)]/2所以S=1/S1+1/S2+...+1/Sn=(1/2)[(1-1/3)+(

ak1,ak2,ak3.构成等比^2=ak1*ak3(a1+d)^2=(a1)*（a1+(6-1)d）计算d=3a1ak4=^2/ak2=a1+(k4-1)*dd为方差(a1+5*d)^2/(a1+d