,an=
(an-1+an-2)(n∈N,且n≥3),则
an的值为A.-2 B.2 C.12 D.
,an=(an-1+an-2)(n∈N,且n≥3),则an的值为A.-2 B.2 C.12 D.
B
解析：将an=(an-1+an-2)左右两边同时减去an-1,得an-an-1=-(an-1-an-2)(n≥3),令bn=an-an-1,则{bn}是以-为公比的等比数列,b3=a3-a2=,
∴bn=
,即an-an-1=
,…,a3-a2=
,a2-a1=-
.
∴an=(an-an-1)+…+(a3-a2)+(a2-a1)+a1
=
=
.
∴
=2.