1. Stating the problem: We want to find how many integers in the sequence 20, 21, 22, ..., 2024, 2025 are multiples of 3 but not multiples of 5. 2. Find all multiples of 3 between 20 and 2025. - The smallest multiple of 3 greater than or equal to 20 is 21 since \(21 \div 3 = 7\). - The largest multiple of 3 less than or equal to 2025 is 2025 since \(2025 \div 3 = 675\). - The multiples of 3 here form an arithmetic sequence \(21, 24, 27, ..., 2025\). - Number of multiples of 3 is \(675 - 7 + 1 = 669\). 3. Find multiples of both 3 and 5 (i.e., multiples of 15) between 20 and 2025. - The smallest multiple of 15 greater than or equal to 20 is 30 since \(15 \times 2 = 30\). - The largest multiple of 15 less than or equal to 2025 is 2025 since \(15 \times 135 = 2025\). - Number of multiples of 15 = \(135 - 2 + 1 = 134\). 4. Count numbers that are multiples of 3 but NOT multiples of 5: \[\text{Count} = 669 - 134 = 535.\] 5. Final answer: \(\boxed{535}\).