Answer
The total score of the player who sinks all the 15 balls is 120 points.
Work Step by Step
The arithmetic series is 1 + 2 + ... + 14 + 15 or $\sum\limits_{n=1}^{15} n$
$\sum\limits_{n=1}^{15} n = \frac{15}{2}(1 + 15) = 120$
The total score of the player who sinks all the 15 balls is 120 points.
