Question

已知等比数列{a}的前5项和为10,前10项和为50,求这个数列的前15项和

Answer 1

设an=a1*q^(n-1)

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

s5=a1*(q^5-1)/(q-1)=10

s10=a1*(q^10-1)/(q-1)=50

两式相除：

q^5+1=5

q^5=4

a1*(q^5-1)/(q-1)=10

a1/(q-1)=10/3

s15=a1*(q^15-1)/(q-1)

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

=63a1/(q-1)

=63*(10/3)

=210