The tip of a colorful triangle

Original source: Problem 1 of British Informatics Olympiad 2017, Round 1

You’re given a bunch of red (R), green (G), and blue (B) balls. I arrange some balls on a line. Then I ask you to complete the triangle of balls under the following simple rules, and tell me the color of the ball at the last row:

• Below two balls of the same color, place a ball of that color. (For example, a G must be placed under two G’s.)
• Below two balls of different colors, place a ball of the third color. (For example, a B must be placed under a R and a G.)

If I gave you the balls "R R G B R G B B", you would place the balls like the following, and tell me "it’s green":

R R G B R G B B
 R B R G B R B
  G G B R G G
   G R G B G
    B B R R
     B G R
      R B
       G

Now, I’ll give you a sequence of 60,000 balls. I won’t even show you all the balls’ colors; the only information available to you is that it starts with 999 balls of the pattern RGB RGB RGB … RGB, and ends with 999 balls of the pattern BGR BGR BGR … BGR.

Using the same rules, can you guess the color of the ball on the last row? The answer is unique, and an answer with mathematical explanation is preferred.