To determine the number that fits best in the sequence 1, 2, 4, 7, 11, 22, we need to analyze the pattern between consecutive numbers.
Starting with the differences:
- 2 – 1 = 1
- 4 – 2 = 2
- 7 – 4 = 3
- 11 – 7 = 4
- 22 – 11 = 11
The differences between the numbers are:
- 1
- 2
- 3
- 4
- 11
Clearly, the first four differences are incrementing by one. After the difference of 4, we see a jump to 11, which seems inconsistent with the previous pattern. However, if we look closely, there’s a missing number after 11 that follows the sequence of increasing differences.
If we apply the established pattern of incrementing the difference by 1, the next difference after 4 should be 5, which when added to 11 would give:
- 11 + 5 = 16
Thus, the sequence would appear as follows: 1, 2, 4, 7, 11, 16, 22. Therefore, 16 is the number that fits best in the sequence before 22.
In conclusion, while there’s a significant leap from 11 to 22, adding 16 maintains the logic of gradual increases in the sequence. Hence, 16 would be a fitting candidate for the missing number.