Analyze the differences between consecutive terms: 6-3=3, 10-6=4, 16-10=6, 24-16=8. The pattern shows differences increasing by 1, then 2, then 2. However, a clearer pattern is: add 3, add 4, add 6, add 8, add 12. Each addition increases by 1, 2, 2, 4... Alternatively, this could be n+3 where n is prime-related. The pattern 3, 4, 6, 8, 12 suggests doubling prime increments. The next term is 24 + 12 = 36.