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Unique geometric sequence with shifted terms

High school · ●●●○○ 50 pts

The geometric sequence {an}\{a_n\} satisfies a1=aa_1=a with a>0a>0, and a1+1a_1+1, a2+2a_2+2, a3+3a_3+3 form a geometric sequence. If {an}\{a_n\} is unique, find the value of aa. Round to two decimal places.

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quadratic equationsdiscriminant