在數(shù)列{an}中,a1=1,a2=5,an+2=an+1-an (n∈N*),則a100等于( an+2=an+1-an,an+3=an+2-an+1,兩式相加可得
在數(shù)列{an}中,a1=1,a2=5,an+2=an+1-an (n∈N*),則a100等于( )方法一:an+2=an+1-an,an+3=an+2-an+1,兩式相加可得an+3=-an,an+6=an,∴a100=a16×6+4=a4=-1.an+6=an,∴a100=a16×6+4=a4=-1.為什么這樣做?