Question

高一数学数列题，过程

1. 设等差数列{an}的公差为-2，如果a1+a4+a7+……a97=50,则a3+a6+a9+……a99=?
2. 已知an为等差数列，S1=1,S4=5,则S6=?
3. 已知数列｛an｝为前n项和Sn=3n(41-n)/2,试求数列{|an|}前30项的和
4. 等差数列｛an｝中，若已知a2=4,a5=-1\2,求an=?

Answer 1

1)a1+a4+a7+……a97=50
a1+2d+a4+2d+a7+2d……a97+2d
=a1+a4+a7+……a97+2d*32
=50-128
=-78
2)S1=1,S4=5
a1=1
S4=a1+a2+a3+a4
=a1+a1+d+a1+2d+a1+3d
=4a1+6d=4+6d=5
d=1/6
S6=S4+a5+a6
=5+a1+4d+a1+5d
=7+9d=7+3/2=17/2
3)Sn=3n(41-n)/2 这是前n项和
所以前30项和s30=3*30(41-30)/2=495
4)a2=4,a5=-1\2
a5-a2=3d=-1/2-4=-9/2
d=-3/2
a1=a2-d=4+3/2=11/2
an=a1+(n-1)d=11/2-3/2n+3/2
=7-3n/2

Answer 2

1)a1+a4+a7+……a97=50
a1+2d+a4+2d+a7+2d……a97+2d
=a1+a4+a7+……a97+2d*32
=50-128
=-78
2)S1=1,S4=5
a1=1
S4=a1+a2+a3+a4
=a1+a1+d+a1+2d+a1+3d
=4a1+6d=4+6d=5
d=1/6
S6=S4+a5+a6
=5+a1+4d+a1+5d
=7+9d=7+3/2=17/2
3)Sn=3n(41-n)/2
所以前30项和s30=3*30(41-30)/2=495
4)a2=4,a5=-1\2
a5-a2=3d=-1/2-4=-9/2
d=-3/2
a1=a2-d=4+3/2=11/2
an=a1+(n-1)d=11/2-3/2n+3/2
=7-3n/2

注意运算