In the number series 1, 3, 6, 10, 15, ?, which number should correctly replace the question mark to continue the pattern?

Introduction / Context:
This problem checks your ability to recognise a classic increasing pattern known as triangular numbers. Such series appear frequently in aptitude tests and competitive examinations, so recognising the underlying idea quickly can save valuable time during the exam.

Given Data / Assumptions:
- The given series is: 1, 3, 6, 10, 15, ?- All terms are positive integers increasing steadily.- The pattern is expected to be simple and based on addition.

Concept / Approach:
For increasing series like this, we first examine the differences between consecutive terms. If those differences themselves follow a simple pattern, we can extend that pattern to find the missing term. In many reasoning exams, sequences like 1, 3, 6, 10, 15 represent the sums of the first few natural numbers and are called triangular numbers.

Step-by-Step Solution:
- Compute the differences: 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, 15 - 10 = 5.- The difference sequence is 2, 3, 4, 5, which clearly increases by 1 each time.- The next difference should therefore be 6.- Add this to the last known term: 15 + 6 = 21.- Hence, the missing term in the series must be 21.

Verification / Alternative check:
- You can view each term as the sum of the first n natural numbers.- 1 = 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, 15 = 1 + 2 + 3 + 4 + 5.- The next term should be 1 + 2 + 3 + 4 + 5 + 6 = 21, confirming our answer.

Why Other Options Are Wrong:
- 20: This would break the pattern of consecutive differences and cannot be expressed as the sum of the first six natural numbers.- 22: Does not follow the difference pattern of +2, +3, +4, +5, +6.- 24: Also inconsistent with both the difference pattern and the triangular number interpretation.

Common Pitfalls:
A common mistake is to assume a constant difference or to miscalculate one of the intermediate sums. Some students also try to use complex formulas where a simple difference pattern is sufficient. Always check the difference sequence first, because many exam series are built directly from it.

Final Answer:
The missing term is 21, so the correct option is 21.