What is the missing number 'X' of the series 7, X, 21, 31, 43?

The given series is 7, X, 21, 31, 43. To find the missing number 'X', let's analyze the differences between consecutive terms.

1. Calculate the differences between the known consecutive terms: 31 - 21 = 10 43 - 31 = 12

2. Observe the pattern in these differences: The differences are 10 and 12. This shows an increase of 2 (12 - 10 = 2). This suggests that the differences between consecutive terms are increasing by 2 each time.

3. Extend this pattern backwards: If the differences are increasing by 2, then the difference before 10 should be 10 - 2 = 8. And the difference before 8 should be 8 - 2 = 6. So, the sequence of differences should be 6, 8, 10, 12.

4. Apply this pattern to find X: The first difference in the series is (X - 7). According to our pattern, this difference should be 6. X - 7 = 6 X = 6 + 7 X = 13

5. Verify the complete series with X = 13: The series becomes: 7, 13, 21, 31, 43. Let's check the differences: 13 - 7 = 6 21 - 13 = 8 31 - 21 = 10 43 - 31 = 12 The differences (6, 8, 10, 12) form an arithmetic progression with a common difference of 2, confirming the pattern.

Therefore, the missing number 'X' is 13.

The final answer is C) 13.