An是公差为d(d不等于0)的等差数列,它的前10项和S10=110且a1,a2,a4,成等比数列.1,证明a1=d 2求公差d的...An是公差为d(d不等于0)的等差数列,它的前10项和S10=110且a1,a2,a4,成等比数列.1,证明a1=d2求公差d的值和数列An的通项公式.

a1*a4=a2*a2 又a4=a1+3*d a2=a1+d
==> a1*a1+3*a1*d=a1*a1+2*a1*d+d*d ==> a1*d=d*d ==> a1=d
S10=10*a1+45*d ==> 55*d=110 ==> d=2
通项公式:an=2+(n-1)*2 ==> an=2n

a1*a4=a2*a2
a1*(a1+3d)=(a1+d)*(a1+d)
a1=d
S10=110 Sn=n*a1+n(n-1)d/2
10d+45d=110
d=2
an=a1+(n-1)d
=2n+1

1、
等比则(a1+d)²=a1(a1+3d)
a1²+2a1d+d²=a1²+3a1d
a1d=d²
d≠0
a1=d
2、
S10=(2a1+9d)*10/2=55d=110
d=2
a1=d=2
an=a1+(n-1)d
所以an=2n

设an=a1+(n-1)d,由S10=110得10a1+45d=110,
又a1,a2,a4,成等比数列，故a2*a2=a1*a4,化简可得a1=d(因为不等于0)。把a1=d代入10a1+45d=110得a1=d=2，所以数列An的通项公式an=2n