Question

已知数列{an}为等比数列，sn是它前n项和。若a2×a3=2a1，且a4与2a7的等差中项为5/4，则s5等于？

A 35 B 33 C 31 D 29

Answer 1

∵a2*a3=a1*a4
∵a1*a4=2a1
∴a4=2
∵a4与2a7的等差中项为5/4
2*5/4=a4+2a7
∴a7=1/4
∵q³=a7/a4=1/8
∴q=1/2
∴a1=a4/q³=16
∴S5=a1*(1-q^5)/(1-q)=31
所以选C

Answer 2

C 31

a2*a3=2a1
a1q*a1q^2=2a1
a1q^3=2
a4=2

a4+2a7=5/4*2=5/2
2+2a7=5/2
2a7=1/2
a7=1/4

a7=a4q^3
1/4=2*q^3
q^3=1/8
q=1/2

a4=a1q^3
2=1/8*a1
a1=16

s5=a1(1-q^5)/(1-q)
=16*[1-(1/2)^5]/(1-1/2)
=16*31/32*2
=31