设等比数列{an}的公比q=2,前n项和为Sn,则S4/a2等于急.

设等比数列{an}的公比q=2,前n项和为Sn,则S4/a2等于急.
设等比数列{an}的公比q=2,前n项和为Sn,则S4/a2等于
急.

设等比数列{an}的公比q=2,前n项和为Sn,则S4/a2等于急.
qSn+a1=Sn+a(n+1)
Sn=a1(1-q^n)/1-q
=a1(2^n-1)
S4/a2=a1*(2^4-1)/2a1=15/2

Sn=a1(1-q^n)/1-q
=a1(1-2^n)/1-2
=-a1(1-2^n)
∴S4=-a1(1-2^4)
=-a1(1-16)
=15a1
又∵a2=2a1
∴S4/a1=15a1/2a1=15/2

a2=a1q,S4=a1(1-q4)/1-q，结果得7.5