The series follows a pattern where each term is multiplied by an increasing integer and then increased by 1: (10 x 1) + 1 = 11, (11 x 2) + 2 = 24, and (24 x 3) + 3 = 75. Following this rule for the next term, calculate (75 x 4) + 4 = 304. Applying the pattern one more time gives (304 x 5) + 5 = 1525.