Question

等比数列{an}中,s4=1,s8=4,则s12=多少?急用!

Answer 1

sn=a1(1-q^n)/(1-q)

a1(1-q^4)/(1-q)=1

a1(1-q^8)/(1-q)=4

(1-q^8)/(1-q^4)=4

q^4+1=4

q^4=3

a1(1-3)/(1-q)=1

a1/(1-q)=-1/2

s12=a1(1-q^12)/(1-q)

=a1/(1-q)*[1-(q^4)^3]

=-1/2*(1-27)

=13