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

• The given series is 7, X, 21, 31, 43.

• Calculate the difference between the known consecutive terms: 31 - 21 = 10 and 43 - 31 = 12.

• The differences are increasing by 2 (10, 12), suggesting the previous difference should be 8.

• Therefore, X - 7 = 8, which implies X = 15. However, let's re-evaluate the pattern.

• Let's check the differences again: 21 - X, 31 - 21 = 10, 43 - 31 = 12. If the pattern of differences is +4, +6, +8, +10, +12, then 7 + 4 = 11, 11 + 6 = 17 (not 21). This doesn't fit.

• Let's look at the differences between the terms provided: 21, 31, 43. The differences are 10 and 12. The next difference would be 14. The previous difference before 10 should be 8.

• If the difference between 7 and X is 8, then X = 15. But 15 is not an option.

• Let's try another pattern. Maybe the differences are 4, 6, 8, 10, 12? 7+4=11, 11+6=17 (No). 7+4=11, 11+10=21? No.

• Let's look at the options. If X=13, the series is 7, 13, 21, 31, 43. Differences: 13-7=6, 21-13=8, 31-21=10, 43-31=12. The differences are 6, 8, 10, 12, which is an arithmetic progression with a common difference of 2.

• This pattern fits perfectly. Thus, X is 13.