在递减的等差数列an中,a2+a4+a6+12,a3*a5+7,前n项和为Sn,（1)求an和Sn(2)令Tn=|a1|+|a2|+...+|an|,求Tn
问题描述：
在递减的等差数列an中,a2+a4+a6+12,a3*a5+7,前n项和为Sn,（1)求an和Sn(2)令Tn=|a1|+|a2|+...+|an|,求Tn
答
(1)
an = a1+(n-1)d
a2+a4+a6=3a1+9d=12 (1)
a3.a5= (a1+2d)(a1+4d)=7 (2)
sub (1) into (2)
(4-3d+2d)(4-3d+4d)=7
16-d^2=7
d=-3 or 3(rejected)
a1=13
an = 13-3(n-1) = 16-3n
Sn = (13 +16-3n)n/2 = (29-3n)n/2
(2)
an >=0
16-3n >=0
n