Consider the numeric sequence: 125, 80, 45, 20, ... What is the next number that should appear in this series?

Introduction:
This question tests your ability to recognize patterns in a number sequence. Such sequences often involve simple arithmetic operations like adding, subtracting, or using a constant difference that itself follows a pattern. Here, we must determine how the terms are changing to predict the next term correctly.

Given Data / Assumptions:

• The sequence starts as: 125, 80, 45, 20, ...
• We must find the next term after 20.
• The pattern is assumed to be consistent throughout the sequence.

Concept / Approach:
First, look at the differences between consecutive terms: 80 − 125, 45 − 80, and 20 − 45. If these differences follow a simple pattern, such as an arithmetic progression, we can then predict the next difference and hence the next term. Recognizing that the differences themselves form a sequence is very common in such problems.

Step-by-Step Solution:
Compute the first difference: 80 − 125 = −45. Compute the second difference: 45 − 80 = −35. Compute the third difference: 20 − 45 = −25. So the sequence of differences is: −45, −35, −25, ... Now examine this difference sequence. The change from −45 to −35 is +10, and from −35 to −25 is also +10. Thus, the differences themselves form an arithmetic progression with common difference +10. The next difference should be: −25 + 10 = −15. To find the next term in the original series, add this next difference to the last term 20. Next term = 20 + (−15) = 5. Therefore, the next number in the sequence is 5.

Verification / Alternative check:
We can now write the extended sequence including the new term: 125, 80, 45, 20, 5. The differences are: −45, −35, −25, −15. The difference of differences remains +10 throughout, confirming the pattern is consistent.

Why Other Options Are Wrong:
A next term of 15, −5, or 10 would produce differences that break the arithmetic pattern of the difference sequence. For example, if the next term were 10, the last difference would be −10, and the step between −25 and −10 would be +15 instead of +10, which does not match the established pattern.

Common Pitfalls:
Some learners look only at the original terms and guess a random rule such as halving or subtracting a fixed number, which does not hold for all terms. Others may miss that the differences form a clear arithmetic series. Always compute and examine the difference sequence when the pattern is not immediately obvious.

Final Answer:
The next number that should appear in the series is 5.