1. The problem involves finding the missing numbers in a 4x3 grid of sequences, where each box contains a sequence with some blanks. 2. To solve this, we analyze each sequence to identify patterns such as arithmetic progressions, geometric progressions, or other relationships. 3. For example, in the top row, the sequence is 0, __, 12, 18, 24. We notice the numbers increase by 6 starting from 12: 12, 18, 24. To find the missing number after 0, we check if the sequence is arithmetic with common difference 6. Since 0 + 6 = 6, the missing number is 6. 4. Similarly, for the second row, 0, __, 22, __, we look for a pattern. If the sequence increases by 11, then the missing numbers are 11 and 33. 5. We continue this process for each row and column, identifying the pattern and filling in the blanks accordingly. 6. The general formula for an arithmetic sequence is $$a_n = a_1 + (n-1)d$$ where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. 7. Using this formula, we calculate each missing term by substituting the known values. 8. After filling all blanks, the completed grid sequences are: - Row 1: 0, 6, 12, 18, 24 - Row 2: 0, 11, 22, 33 - Row 3: 8, 15, 19, 23 - Row 4: 16, 29, 36, 43 - Row 5: 4, 9, 11, 13 - Row 6: 5, 20, 50, 86 - Row 7: 7, 21, 38, 55 - Row 8: 3, -10, -21, -33 - Row 9: -180, -216, -239, -253 - Row 10: 50, 62, 89, 116 - Row 11: 45, 71, 143, 215 This completes the missing numbers in the grid.