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•(

5
3
)n−1
B. 5•(
3
5
)n−1

C. 3•(
3
5
)n−1

D. 3•(
5
3
)n−1

∵{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

9
2
d,
∴q=
a5+3d
a5
=
15
2
d
9
2
d
=
5
3

∵b2=5,q=
5
3

∴b1=
b2
q
=3,
bnb1qn−1=3•(
5
3
)
n−1

故选D