Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 659: 43

For Player A, the score is $45$ points. For Player B, the score is $75$ points.

For Player A, the score is 1 + 2 + ... + 8 + 9, which is equal to $\frac{9}{2}(1 + 9) = 45$ points. For Player B, the score is 10 + 11 + ... + 14 + 15, which is equal to the total score from 1 to 15 minus the total score from 1 to 9, that is, $\frac{15}{2}(1 + 15) - \frac{9}{2}(1 + 9) = 120 - 45 = 75$ points.