State the limit for the following sequences

2/2 , 2/4 , 2/8 , 2/16 , 2/32

Hector and alex traded video games. alex gave hector one fourth of his video games in exchange for 6 video games. then he sold 3 video games and gave 2 video games to his brother. alex ended up with 16 video games. how many video games did alex have when he started?

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.