已知an为等差数列 公差d不等于0

a(n)=a+(n-1)d,d不为0.[a(3)]^2=a(1)a(9)=a[a+8d]=[a+2d]^2,0=a^2+8ad-a^2-4ad-4d^2=4ad-4d^2=4d(a-d),0=a-d.

设等差数列的公差为d,a1,a3,a13成等比数列,则(a3)²=a1•a13(1+2d)²=1+12d,4d²=8d.因为公差不为0,所以d=2.从而an=

显然有：an=a1+(n-1)d,bn=b1*q^(n-1),又a3=b3,a7=b5,所以：a1+2d=a1*q^2,①a1+6d=a1*q^4,②由上面2个式子,得到：3①-②：2a1=a1*(3

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

a1,a3,a9成等比数列a3^2=a1*a9(a1+2d)^2=a1*(a1+8d)解得a1=d(a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13d/16d=

1.S5=5a1+10d=5(a1+2d)=70a1+2d=14a3=14a7^2=a2×a22(a3+4d)^2=(a3-d)(a3+19d)a3=14代入,整理,得d(d-4)=0d=0(已知d不

已知等差数列an的公差d不等于0,它的前n项和为Sn,若…4018

由题知：(a1+2d)(a1+14d)=(a1+8d)^2化简得到：(a1)^2+16a1*d+28d^2=(a1)^2+16a1*d+64d^236d^2=0解得：d=0因为d≠0故无解

已知公差为d(d不等于0）,a1=1,那么：a2=a1+d=1+d,a5=a1+4d=1+4d,a14=a1+13d=1+13d又a2a5a14依次成等比数列,所以：(a5)²=a2*a14

1.S5=5a1+10d=5(a1+2d)=70a1+2d=14a3=14a7^2=a2×a22(a3+4d)^2=(a3-d)(a3+19d)a3=14代入,整理,得d(d-4)=0d=0(已知d不

因为a5=a1+4d,a9=a1+8d,a15=a1+14d且a5a9a15成等比数列所以(a1+8d)^2=(a1+4d)(a1+14d)即(a1)^2+16a1*d+64d^2=(a1)^2+18

再问：求k1+2k2+3k3+.......+nkn=多少再答：令S=k1+2k2+...+nkn=2*[3^0+2*3^1+3*3^2+………+n*3^(n-1)]-(1+n)n/2令T=3^0+2

ak=48+2kbk=10+(k-1)dSk=(48+2k)[10+(k-1)d]令SK≤21即(48+2k)[10+(k-1)d]≤21求出k来.再问：最大圆面积为Sk

a1*a17=a5^2a1(a1+16d)=(a1+4d)^2a1^2+16a1d=a1^2+8a1d+16d^216d^2-8a1d=08d(2d-a1)=0a1=2d2d,3d,4d,5d,6d,

问题是什么?对于Sn,Sn为=等差数列与等比数列的对应各项积,所以Sn-qSn=a1b1+db2+db3+...+dbn-db(n+1)推出Sn=...对于Tn,Tn=Sn-2a1b1-2a4b4-2

【解】（1）方程A(k)(X^2)+2A(k+1)X+A(k+2)=0,则其Δ=4[A(k+1)^2-A(k)*A(k+2)]=4[[A(k)+d]^2-A(k)*[A(k)+2d]]=4d^2>0;

因为{An}是等差数列,所以A2+A8=A4+A6=10,A4*A6=24,所以可将A4、A6看作方程x^2-24x+10=0的两个根,因为d

依题意,有:a3*a9=a7^2即(a1+2d)(a1+8d)=(a1+6d)^2解得:d=-0.1d因此a1+a6=2a1+5d=1.5da2+a3=2a1+3d=1.7d则(a1+a6)/(a2+

先求An的通项就行了A1+A4=14A2A3=45d

证明：左边＝1/(a1a2)+1/(a2a3)+...+1/(an-1*an)＝1/d(1/a1-1/a2)+1/d(1/a2-1/a3)+...+1/d(1/an-1-1/an)=1/d[(1/a2