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 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.

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