\(3^{n-1}\) Terms in a Group

Algebra Level 1

Consider a group sequence of positive integers \[(1),(2,3,4),(5,6,7,8,9,10,11,12,13), \dots,\] where the \(n ^{\text{th}}\) group has \(3^{n-1}\) terms in it. If \(1068\) is the \(b^{\text{th}}\) term of the \(a^{\text{th}}\) group, what is \(a+b\)?

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