an=2a(n-1)+2×(-1)^n
an-(2/3)×(-1)^n=2a(n-1)+(4/3)×(-1)^n
an-(2/3)×(-1)^n=2[a(n-1)-(2/3)×(-1)^(n-1)]
即:[an-(2/3)×(-1)^n]/[a(n-1)-(2/3)×(-1)^(n-1)]=2=常数,则:
数列{an-(2/3)×(-1)^n}是以a1-(2/3)×(-1)=a1+(2/3)=5/3为首项、以q=2为公比的等比数列,则:
an-(2/3)×(-1)^n=(5/3)×2^(n-1)
得:an=(5/3)×2^(n-1)+(2/3)×(-1)^n