Understanding the Number Series Pattern

The question asks us to find the missing number in the given numerical sequence: 31, 20, 7, -8, -25, ?

To solve this, we need to identify the underlying pattern or rule governing the series.

Step-by-Step Solution for the Series Pattern

First, let's examine the differences between consecutive terms:

• Difference between the first term (31) and the second term (20): $20 - 31 = -11$
• Difference between the second term (20) and the third term (7): $7 - 20 = -13$
• Difference between the third term (7) and the fourth term (-8): $-8 - 7 = -15$
• Difference between the fourth term (-8) and the fifth term (-25): $-25 - (-8) = -25 + 8 = -17$

Identifying the Pattern in the Differences

The sequence of differences we obtained is: -11, -13, -15, -17.

Let's look at the differences between these consecutive differences:

• $-13 - (-11) = -13 + 11 = -2$
• $-15 - (-13) = -15 + 13 = -2$
• $-17 - (-15) = -17 + 15 = -2$

We observe a consistent difference of $-2$. This indicates that the amount subtracted from the previous term increases by 2 in each step.

Calculating the Missing Term

To find the next term in the original series, we first need to determine the next difference in the sequence of differences.

Following the pattern, the next difference after -17 should be:

Now, we apply this difference to the last term of the original series (-25) to find the missing number:

Missing Term = Last Term + Next Difference

Missing Term = $-25 + (-19)$

Missing Term = $-25 - 19$

Missing Term = $-44$

Conclusion

Based on the analysis of the pattern, the number that should logically follow in the series 31, 20, 7, -8, -25 is -44.