数列{an}是公差不为零的等差数列,并且a5,a8,a13是等比数列{bn}的相邻三项.若b2=5,则bn=( ) A.5•(53)n−1 B.5•(35)n−1 C.3•(35)n−1 D.3•(53)n−1
问题描述:
数列{an}是公差不为零的等差数列,并且a5,a8,a13是等比数列{bn}的相邻三项.若b2=5,则bn=( )
A. 5•(
)n−15 3
B. 5•(
)n−13 5
C. 3•(
)n−13 5
D. 3•(
)n−1 5 3
答
∵{an}是公差不为零的等差数列,并且a5,a8,a13是等比数列{bn}的相邻三项,
∴(a5+3d)2=a5(a5+8d),
∴a5=
d,9 2
∴q=
=
a5+3d a5
=
d15 2
d9 2
,5 3
∵b2=5,q=
,5 3
∴b1=
=3,b2 q
∴bn=b1qn−1=3•(
)n−1.5 3
故选D