Question

在正项等比数列的前N项和为SN,若S3=6,a7+a8+a9=24,则S30=

Answer 1

设公比为q

S3=a1(1-q^3)/(1-q)=6...(1),

a7+a8+a9=24,

得S9-S6=a1(1-q^9)/(1-q)-a1(1-q^6)/(1-q)=24..(2)

解(1)(2)方程得

q^3=2,a1=6(q-1)

S30=a1(1-q^30)/(1-q)

=6(q-1)(1-q^30)/(1-q)

=6(q^30-1)

=6*(2^10-1)