Question

which number is missing in this series?
1 3 7 21 31 43

Answer 1

To find the missing number in the series \(1, 3, 7, 21, 31, 43\), let's analyze the differences between consecutive numbers:

- \(3 - 1 = 2\)
- \(7 - 3 = 4\)
- \(21 - 7 = 14\)
- \(31 - 21 = 10\)
- \(43 - 31 = 12\)

The differences are: \(2, 4, 14, 10, 12\).

Looking more closely at the differences, we may notice they don't follow a simple arithmetic progression. However, observing the numbers more deeply might reveal a pattern.

Let's rewrite the series and check for any possible patterns:
- \(1\)
- \(3 = 1 + 2\)
- \(7 = 3 + 4\)
- \(21 = 7 \times 3\) or \(7 + 14\)
- \(31 = 21 + 10\)
- \(43 = 31 + 12\)

It appears that the jump between \(7\) to \(21\) is significant, as it can be expressed through multiplication by \(3\) (or we may also say \(7 + 14\)).

To see if there's a consistent operation or pattern, let's consider where a missing number might logically fit.

If we hypothesize that the missing number is between \(7\) and \(21\), one realistic number is \(11\) (chosen as \(10 + 1\) to keep an increment relative).

Then, we can propose the sequence would be:
- \(1\)
- \(3\)
- **\(11\) (missing number)**
- \(21\)
- \(31\)
- \(43\)

Let’s check the possible newer differences:
- \(3 - 1 = 2\)
- \(11 - 3 = 8\)
- \(21 - 11 = 10\)
- \(31 - 21 = 10\)
- \(43 - 31 = 12\)

This seems a bit more organized and manageable.

Thus, it seems logical that the missing number could be \(11\) in a proposed structured format.

So, the missing number in the sequence is:
**11**