Question

等比数列求和题在等比数列An中,S3=3.5,S6=31.5,求An

Answer 1

s6=a1+a2+a3+a4+a5+a6

=a1+a2+a3+q^3(a1+a2+a3)

31.5=3.5+3.5q^3

3.5q^3=28

q^3=8

q=2

s3=a1+a2+a3

=a1+a1q+a1q^2

=a1(1+q+q^2)

=a1(1+2+4)

=7a1

7a1=3.5

a1=0.5=1/2

an=a1q^n-1

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

=2^(n-2)