问题
选择题
己知{an}(n∈N*)为等差数列,其公差为-2,且a7是a3与a9的等比中项,则{an}的首项a1=( )
A.14
B.16
C.18
D.-20
答案
∵{an}(n∈N*)为等差数列,其公差为-2,
∴a7=a1+12,a3=a1+4,a9=a1+16,
∵a7是a3与a9的等比中项,
∴(a1+12)2=(a1+4)(a1+16),
解得a1=-20.
故选D.
己知{an}(n∈N*)为等差数列,其公差为-2,且a7是a3与a9的等比中项,则{an}的首项a1=( )
A.14
B.16
C.18
D.-20
∵{an}(n∈N*)为等差数列,其公差为-2,
∴a7=a1+12,a3=a1+4,a9=a1+16,
∵a7是a3与a9的等比中项,
∴(a1+12)2=(a1+4)(a1+16),
解得a1=-20.
故选D.