Question

已知等比数列{An}的前n项和为Sn,求证S6,S12-S6,S18-S12也成等比数列

Answer 1

等比数列的和

Sn = a(1-q^n)/(1-q)

S6 = a(1-q^6)/(1-q)

S12 =a(1-q^12)/1-q)

S18 =a(1-q^18)/(1-q)

S12-S6=aq^6(1-q^6)/(1-q)

S18-S12=aq^12(1-q^6)/(1-q)

满足(S12-S6)²=S6×(S18-S12)

所以S6,S12-S6,S18-S12也成等比数列