若数列{an}为等差数列,公差为1/2,且S100=145,则a2+a4+...+a100=
问题描述:
若数列{an}为等差数列,公差为1/2,且S100=145,则a2+a4+...+a100=
答
Sn=a1*n+n(n-1)d/2
145=a1*100+100*99*1/4
a1=-23.3
a2=-22.8
a2 a4 a6...a100可以看成以-22.8为首项 1为公差的等差数列
a2+a4+...+a100=(-22.8+26.2)*50/2=85
答
a1+a3+a5+...+a99=s1;a2+a4+...+a100=s2;s1+s2=s100=145,
s1=50*a1+50*(50-1)d,s2=50*a1+50*50*d;
100a1+50*49*0.5+50*50*0.5=145
a1=-23.3代入得s2=50*(25-23.3)=85