Question

a1=20. s10=s15当n取何值时sn最大。并求出最大值。。

Answer 1

(a1+a10)*10/2=(a1+a15)*15/2
(a1+a1+9d)*5=(a1+a1+14d)*15/2
(2a1+9d)*5=(2a1+14d)*15/2
(2a1+9d)*5=15(a1+7d)
2a1+9d=3(a1+7d)
2*20+9d=3(20+7d)
40+9d=60+21d
12d=-20
3d=-4
d=-4/3

sn=[2a1+(n-1)d]*n/2
=[2*20+(n-1)*(-4/3)]*n/2
=[20+(n-1)*(-2/3)]*n
=20n+n(n-1)*(-2/3)
=20n-2n^2/3+2n/3
=-2n^2/3+62n/3
=-2/3(n^2-31n)
=-2/3(n^2-31n+961/4)+961/4*2/3
=-2/3(n-31/2)^2+961/6
当n=16或n=15时，Sn值最大
Sn最大=-2/3*1/4+961/6
=-1/6+961/6
=960/6
=160

s4=(a1+a4)*4/2
=(a1+a1+3d)*2
=2(2a1+3d)
2(2a1+3d)=24
2a1+3d=12................1

s5-s2
=a3+a4+a5
=a1+2d+a1+3d+a1+4d
=3a1+9d
3a1+9d=27
a1+3d=9.....................2

1式-2式得
a1=3
将a1=3代入2式得
a1+3d=9
3+3d=9
3d=6
d=2

an=a1+(n-1)d
=3+(n-1)*2
=2n+1

追问

可以把公式写上麽？我算的d怎么等于-5/3

追答

给个好评吧亲！