Question

在等比数列｛an｝中,若s3=12 s6=36,则s9=

Answer 1

S3=a(1-q^3)/(1-q)=12

S6=a(1-q^6)/(1-q)=a(1-q^3)(1+q^3)/(1-q)=36

相除

1+q^3=3

q^3=2

带入a(1-q^3)/(1-q)=12

a/(1-q)=-12

S9=a(1-q^9)/(1-q)

=[a/(1-q)][1-(q^3)^3]

=-12*(1-8)

=84