等比数列{an}前n项和为Sn若S4=1,S8=4则a13+a14+a15+a16=

等比数列{an}前n项和为Sn若S4=1,S8=4则a13+a14+a15+a16=
等比数列{an}前n项和为Sn若S4=1,S8=4则a13+a14+a15+a16=

等比数列{an}前n项和为Sn若S4=1,S8=4则a13+a14+a15+a16=
S4=a1*(q^4-1)/(q-1)=1
S8=a1*(q^8-1)/(q-1)=4
S8/S4=(q^8-1)/(q^4-1)=4
(q^4+1)(q^4-1)/(q^4-1)=4
q^4+1=4
q^4=3
a1(q^4-1)/(q-1)=1
a1/(q-1)=1/(q^4-1)=1/2
a13+a14+a15+a16
=S16-S12
=a1(q^16-1)/(q-1)-a1(q^12-1)/(q-1)
=[a1/(q-1)]*(q^16-1-q^12+1)
=1/2*(3^4-3^3)
=27