Combined Arithmetic Geometric Progression

Algebra Level 4

We have three numbers in an arithmetic progression, and another three numbers in a geometric progression. Adding the corresponding terms of the two series, we get $120 , 116 , 130$ . If the sum of all the terms in the geometric progression is $342$ , what is the largest term in the geometric progression?

Details and Assumptions:

If the terms of the AP are A, B, C, and the terms of the GP are X, Y, Z, then adding the corresponding terms will give us A+X, B+Y, C+Z.