Positive numbers a1, a2, a3 are in arithmetic progression, while positive numbers g1, g2, g3 are in geometric progression. Given that a1 + g1 = 26, a2 + g2 = 50, a3 + g3 = 114, and a1 + a2 + a3 = 60, find both progressions.

***Please note the 1, 2 and 3 are meant to be subscripts