Arithmetic progression attribute: S 1+S2=2xS3.
Generation: a1(1-q)/(1-q)+a1(1-q 2)/(1-q) = 2xa/kloc-0.
Simplification: when q is not equal to 1, the approximate score is 1-Q+ 1-Q 2 = 2-2Q 3.
Solve the equation: 2Q 3-Q 2-Q = 0. Because the geometric series q is not equal to 0, cut off q.
2Q 2-Q- 1 = 0, and the solution is: q= 1 or q=- 1/2. Because q is not equal to 1, it is concluded that q=- 1/2 is the final solution.
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Where q is 1, which is invalid during verification. In the hypothesis method, it can be assumed that the sequence is 222 ... then S 1=2 S2=4 S3=6, which does not meet the known conditions, so q= 1 does not hold.