Question

求解2012南通二模数学填空题第14题

Answer 1

解：
设首项为2n,公差为2m,
则4个数为 2n,2n+2m,2n+4m,88+2n, q=(2n+4m)/(2n+2m)=(n+2m)/(n+m)
所以 (2n+4m)²=(2n+2m)(88+2n)
(n+2m)²=(n+m)(44+n)
4m²+3mn=44m+44n
n=4m(m-11)/(44-3m)>0
所以 11<m<44/3
m=12,13,14
(1) m=12, n=6
所以 q=(6+24)/(6+12)=5/3
(2) m=13, n不是整数，舍去
(3) m=14,n=56*3/2=84
q=(84+28)/(84+14)=112/98=8/7

所以 q的集合是{5/3,8/7}

Answer 2

不会啊。