Old problem but good

The common ratio in the geometric sequence is ${x\over 1} =x$ . so $y= x^2$ . And the common ratio in arithmetic sequnce is y-x = 3 - y . then we get $2x^2 - x - 3 = 0$ . So we getget $x= {3\over 2}$ or x=-1 . and $y= {9\over 4}$ or $y =1$ . then we get $x+y= {15\over 4}$ or 0 . then the maximum value is 3.75. . so sorry for my bad LaTeX write . I try to improve it