(2008•閘北區(qū)一模)已知數(shù)列{a
n}和{b
n}滿(mǎn)足:a
1=λ,a
n+1=
an+n-4,bn=(-1)n(an-3n+21),其中λ為實(shí)數(shù),n為正整數(shù).S
n為數(shù)列{b
n}的前n項(xiàng)和.
(1)對(duì)任意實(shí)數(shù)λ,證明:數(shù)列{a
n}不是等比數(shù)列;
(2)對(duì)于給定的實(shí)數(shù)λ,試求數(shù)列{b
n}的通項(xiàng)公式,并求S
n.
(3)設(shè)0<a<b(a,b為給定的實(shí)常數(shù)),是否存在實(shí)數(shù)λ,使得對(duì)任意正整數(shù)n,都有a<S
n<b?若存在,求λ的取值范圍;若不存在,說(shuō)明理由.