已知数列{an}为等比数列,Sn是它的前n项和,若a2*a3=2a1,且a4与2a7的等差中项为5⼀4,则S5为多少

2025-06-29 07:50:24
推荐回答(2个)
回答1:

a2*a3=2a1即a1q*a1q^2=2a1 即有a1q^3=2
a4与2a7的等差中项为5/4
a1q^3+2a1q^6=5/4*2
联立求解:a1= 16 q=1/2
S5=1

回答2:

a1²q^3=2a1
a1q^3=2
a4 =2
a4+2a7=2*5/4=5/2
2+2a7=5/2
a7=1/4
a7/a3=1/8=q^3
q=1/2
a1=16
S5=16+8+4+2+1=31