5 设数列｛an｝的前n项和为Sn,a1=1,a2=2,且a(n+2)=an+3(n=1,2,3……),则S100=
问题描述：
5 设数列｛an｝的前n项和为Sn,a1=1,a2=2,且a(n+2)=an+3(n=1,2,3……),则S100=
答
∵a[n+2]=a[n]+3 (n=1,2,3,...)∴a[n+2]-a[n]=3当n=2k-1(k=1,2,3,...),即n是奇数时：∵a1=1∴{a[2k-1]}是首项为1公差为3的等差数列其通项公式是：a[m]=1+3(m-1)=3m-2其前 m项和是：D[m]=m(1+3m-2)/2=m(3m-1)/2∵项数...