In the number series 2, 4, 12, 48, 240, decide whether the last term 240 correctly continues the pattern of the previous terms.

Introduction / Context:

This question is slightly different from typical missing term problems. Instead of asking for a new number, it asks us to validate whether the last term in the series is consistent with the established pattern. Such validation questions test both the ability to infer a rule and the capacity to check that a given term satisfies that rule without assuming it is always correct.

Given Data / Assumptions:

• The series is 2, 4, 12, 48, 240.
• We must decide if 240 is the correct term that follows from 2, 4, 12, and 48.
• The numbers grow quickly, suggesting a multiplicative pattern.
• We assume that there is a simple, uniform rule generating each new term from the previous one.

Concept / Approach:

To validate the last term, we must first uncover the governing rule from the earlier part of the series and then see if that same rule transforms 48 into 240. The pattern appears to involve multiplying each term by an increasing integer factor. By carefully examining these factors between each pair of terms, we can determine if 240 is the correct result of applying the next factor in the sequence to 48.

Step-by-Step Solution:

Step 1: From 2 to 4, the multiplier is 2 since 2 * 2 = 4. Step 2: From 4 to 12, the multiplier is 3 since 4 * 3 = 12. Step 3: From 12 to 48, the multiplier is 4 since 12 * 4 = 48. Step 4: These multipliers form the sequence 2, 3, 4, which suggests that the next multiplier should be 5. Step 5: Apply this multiplier to 48: 48 * 5 = 240, which matches the given last term.

Verification / Alternative check:

If we write the series using the rule explicitly, we have 2, 2 * 2 = 4, 4 * 3 = 12, 12 * 4 = 48, 48 * 5 = 240. The factors 2, 3, 4, 5 are consecutive integers, and there is no irregularity in the pattern. Therefore, 240 is exactly the number we would derive from applying the rule, and there is no reason to doubt its correctness. If 240 were wrong, it would not be obtainable from 48 by multiplying with the next integer in this obvious factor sequence.

Why Other Options Are Wrong:

The option that claims the series is incorrect cannot be accepted, because we have found a clear and simple pattern that fits every term. The options stating that the pattern cannot be determined or that there is no consistent pattern ignore the straightforward use of successive integer multipliers. The suggestion that some other value should replace 240 is also invalid, because replacing 240 with another number would break the neat rule of multipliers 2, 3, 4, 5.

Common Pitfalls:

Some learners may overthink and look for more complex rules, such as combinations of addition and multiplication, when a direct pattern in the multipliers is sufficient. Others may prematurely judge the last term as suspicious simply because it is large. It is important to systematically examine each pair of consecutive terms and confirm whether the multiplier pattern is stable and logical before deciding on correctness.

Final Answer:

The last term 240 is indeed produced by multiplying 48 by 5, so the correct conclusion is Correct, it follows the pattern.