Question

设等比数列{an}的前n项和为Sn,若S2=3,S4=15,则S6=?

Answer 1

Sn=a1(1-q^n)/1-q

S2=a1(1-q^2)/1-q=3
S4=a1(1-q^4)/1-q=15
a1=1 q=2或a1=-3 q=2
S6=a1(1-q^6)/1-q=63

Answer 2

a(n) = aq^(n-1),

3 = s(2) = a + aq,
15 = s(4) = s(2) + aq^2 + aq^3 = a+aq + (a+aq)q^2 = 3 + 3q^2,
q^2 = 4
s(6) = s(4) + aq^4 + aq^5 = 15 + q^4(a+aq) = 15 + 3*4^2 = 15 + 48 = 63

Answer 3

数列是等比数列，S2，S4-S2，S6-S4成等比数列
(S4-S2)²=S2·(S6-S4)
S6=(S4-S2)²/S2
+S4
=(15-3)²/3
+15
=63

Answer 4

a1+a2=3
a1+a2+a3+a4=15,a1+a2+[a1+a2]q*q=15,q=2
a1+a2+a3+a4+a5+a6=15+q*q*q*q[a1+a2]=15+16*3=63