Race against time!

Algebra Level 4

Suppose \(a,b,c\) are real numbers that are in an arithmetic progression (in that order) such that \(a>b>c\).

And \({a}^{2}\), \({b}^{2}\) and \({c}^{2}\) are in a geometric progression (in that order) .

If \(a+b+c=\frac { 3 }{ 2 } \), what is the value of \(a\)?

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