Question

在等比数列{an}中,S3=7/4,S6=63/4,求an

Answer 1

s3=a1(1-q^3)/(1-q)

s6=a1(1-q^6)/(1-q)

s6/s3=(1-q^6)/(1-q^3)

(63/4)/(7/4)=(1+q^3)(1-q^3)/(1-q^3)

1+q^3=9

q^3=8

q=2

s3=a1(1-q^3)/(1-q)

7/4=a1(1-2^3)/(1-2)

7/4=7a1

a1=1/4

an=a1q^(n-1)

=1/4*2^(n-1)

=2^(n-3)