等比数列已知A3=2分之3,和S3=2分之9,求A1和q.

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等比数列已知A3=2分之3,和S3=2分之9,求A1和q.

A3 = A1 * q² = 3/2 ①
S3 = A1 * (1 - q³) / (1 - q) = 9/2 ②
②/① 得
(1 - q³) / (q² - q³) = 3
-> (q - 1)² * (2q + 1) = 0
-> q = 1 ,A1 = 3/2 或 q = -3/2 ,A1 = 6