问题
选择题
已知数列{an}是公比q≠1的等比数列,则在“(1){anan+1};(2){an-an+1}; (3){an3};(4){nan}”这四个数列中,成等比数列的个数是( )
A.1
B.2
C.3
D.4
答案
{an}是公比q≠1的等比数列,则有
=q (q≠1)an+1 an
对于数列{anan+1},
=an+1an+2 anan+1
=q2,是定值,成等比数列.an+2 an
对于数列 {an-an+1},
=an-an+1 an+1-an+2
=an(1-q) an+1(1-q)
=an an+1
,是定值,成等比数列.1 q
对于数列{an3},
=(an+13 an3
)3=q3,是定值,成等比数列.an+1 an
对于数列{nan},
=(n+1)an+1 nan
q,s是与n有关的变量,不成等比数列.n+1 n
成等比数列的个数是3个.
故选C.