Number Series Solution: Find Missing Terms

The task is to find the numbers that replace the question marks (?) in the given number series: 1, 2, 4, ?, 11, ?, 22. We need to determine the underlying pattern of the sequence to find the missing values.

Analyzing the Number Series Pattern

Let's look at the relationship between consecutive numbers in the series:

• The first term is 1.
• The second term is 2. The difference is $2 - 1 = 1$.
• The third term is 4. The difference is $4 - 2 = 2$.

We notice a pattern in the differences: the difference increases by 1 each time. The differences are 1, 2, ... This suggests the next difference might be 3.

Step-by-Step Calculation for Missing Numbers

Let's apply this pattern step-by-step to find the missing numbers:

1. First Question Mark (?): The difference between the third term (4) and the fourth term (the first ?) should be 3. So, the first ? = $4 + 3 = 7$.
2. Checking the Next Term: The fifth term is given as 11. The difference between the fourth term (7) and the fifth term (11) should be $3 + 1 = 4$. Let's check: $7 + 4 = 11$. This matches the given fifth term, confirming our pattern.
3. Second Question Mark (?): The difference between the fifth term (11) and the sixth term (the second ?) should be $4 + 1 = 5$. So, the second ? = $11 + 5 = 16$.
4. Checking the Last Term: The seventh term is given as 22. The difference between the sixth term (16) and the seventh term (22) should be $5 + 1 = 6$. Let's check: $16 + 6 = 22$. This matches the given seventh term, further validating the pattern.

The pattern is confirmed: start with 1, then add 1, then add 2, then add 3, then add 4, then add 5, and finally add 6.

Conclusion on Missing Numbers

The calculated values for the question marks are:

• First ?: 7
• Second ?: 16

Thus, the numbers 7 and 16 correctly replace the question marks in the series. The complete series is 1, 2, 4, 7, 11, 16, 22.