How much XP is required to gain each player level in Apex Legends?

No. The amount continues to increase until level 25.

From level 25 to 100 it is a fixed value = 18.000 xp per level

Level     XP    Total
    1      0        0
    2    100      100
    3   2650     2750
    4   3900     6650
    5   4750    11400
    6   5600    17000
    7   6350    23350
    8   7100    30450
    9   7850    38300
   10   8150    46450
   11   8600    55050
   12   9050    64100
   13   9500    73600
   14   9950    83550
   15  10400    93950
   16  10850   104800
   17  11300   116100
   18  11750   127850
   19  12200   140050
   20  12650   152700
   21  13100   165800
   22  13450   179250
   23  13800   193050
   24  14150   207200
   25  14500   221700
   26  18000   239700
    …      …        …
  100  18000  1571700
  max  18000        ∞