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A cricket player n(n lt 1) matches durin...

A cricket player `n(n lt 1)` matches during his career and made a total of `((n^2-12n+39)(4.6^n-5.3^n+1))/5` runs. If `T_r` represent the runs made by the player in `r^(th)` match such that `T_1 = 6 and T_r=3 T_(r-1) + 6^r,2 leq r leq n` then find n.

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