3 n 1 3^{n-1} Terms in a Group

Algebra Level 2

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

712 709 711 710

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