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1. Unique geometric sequence with shifted terms ●●●○○ 50 ptsThe geometric sequence $\{a_n\}$ satisfies $a_1=a$ with $a>0$, and $a_1+1$, $a_2+2$, $a_3+3$ form a geometric sequence. If $\{a_n\}$ is unique, find the value of $a$. Round to two decimal places.