To fill in the blanks in the sequence {1, 2, _, 4, 6, _, 12, _, 21, 28, 42, 84}, let's first analyze the given numbers:
- The given numbers appear to be factors of 84, as 84 is the largest number present, and the other numbers listed are indeed factors of 84.
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
Based on the factors of 84, we can fill in the missing blanks:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
So, the missing factors are 3, 7, and 14.