等比数列{an}的前n项和为Sn,若4S3-3a3=0公比q=?

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等比数列{an}的前n项和为Sn,若4S3-3a3=0公比q=?
等比数列{an}的前n项和为Sn,若4S3-3a3=0公比q=?

等比数列{an}的前n项和为Sn,若4S3-3a3=0公比q=?
4S3-3a3=0
4(a1+a2+a3)-3a3=0
4a1+4a2+a3=0
a2=a1*q ,a3=a1*q2
4a1*q+4a1+a1*q2=0
a1≠0
4q+4+4q2=0
q=-2

4(a1+a1q+a1q^2)-3a1q^2=0,q^2+4q+4=0,所以q=-2

Q = 1时(≠0)
S3 = 3A1
S2 = 2A1
S3 +3 S2 = 0
A1 = 0(四舍五入)
Q = - 1
S3 = A1
S2 = 0
S3 +2 S2 = 0
A1 = 0(四舍五入)
| Q |≠1时和q≠0 /> S3 = A1(1-Q ^ 3)/(1-Q)=...

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Q = 1时(≠0)
S3 = 3A1
S2 = 2A1
S3 +3 S2 = 0
A1 = 0(四舍五入)
Q = - 1
S3 = A1
S2 = 0
S3 +2 S2 = 0
A1 = 0(四舍五入)
| Q |≠1时和q≠0 /> S3 = A1(1-Q ^ 3)/(1-Q)= A1(1 + Q + Q 2)
S2 = A1(1-Q 2)/(1-Q)= A1(1 + Q)
S3 3 S2 = 0
A1(4 4 Q + Q 2)= 0
4 4 Q + Q 2 = 0
Q = -2

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