已知等比数列{an}满足a1=2，a1+a3+a5=14，则1a1+1a3+1a5=（）A.78B.74C.139D.1318

Question

已知等比数列{a_n}满足a₁=2，a₁+a₃+a₅=14，则

(1)/(a1)+(1)/(a3)+(1)/(a5)=（　　）

A.

(7)/(8)

B.

(7)/(4)

C.

(13)/(9)

D.

(13)/(18)

Answer 1

∵等比数列{a_n}满足a₁=2，a₁+a₃+a₅=14，
∴2+2q²+2q⁴=14，
解得q²=2或q²=-3（舍），
∴(1)/(a1)+(1)/(a3)+(1)/(a5)=(1)/(2)+(1)/(2q2)+(1)/(2q4)=(1)/(2)+(1)/(4)+(1)/(8)=(7)/(8)．
故选：A．