In the number series 2, 4, 12, 48, 240, ( ... ), each term is obtained by multiplying the previous term by increasing integers. What is the next term?

Introduction / Context:
This question presents a number series where each term is obtained from the previous term by multiplication with a changing factor. Recognizing the sequence of multipliers is key to finding the next term. Such series are common in aptitude tests and help assess pattern recognition and basic multiplication skills.

Given Data / Assumptions:

• The given series is 2, 4, 12, 48, 240, ( ... ).
• We are asked to find the next term in the series.
• The numbers grow quickly, suggesting that each term is a multiple of the previous one.

Concept / Approach:
To determine the pattern, calculate the ratio of each term to the previous term. If these ratios form a simple sequence, such as consecutive integers, then we can extend that pattern to find the next multiplier and thus the next term. Here, the ratios turn out to be 2, 3, 4, and 5, which suggests multiplying by the next integer, 6, for the next term.

Step-by-Step Solution:
Compute the ratio of the second term to the first term: 4 / 2 = 2. Compute the ratio of the third term to the second term: 12 / 4 = 3. Compute the ratio of the fourth term to the third term: 48 / 12 = 4. Compute the ratio of the fifth term to the fourth term: 240 / 48 = 5. Thus the multipliers are 2, 3, 4, and 5 in order. The pattern seems to be that each term is multiplied by the next integer: 2, then 3, then 4, then 5. Following this pattern, the next multiplier should be 6. Therefore, the next term = 240 * 6 = 1440. So the required next term in the series is 1440.

Verification / Alternative Check:
We can reconstruct the series using the multipliers to verify. Starting from 2, multiply by 2 to get 4. Multiply 4 by 3 to get 12. Multiply 12 by 4 to get 48. Multiply 48 by 5 to get 240. The pattern clearly holds. If we now multiply 240 by 6, we get 1440, and this fits the expected progression. There are no irregularities or breaks in the multiplier pattern, so this confirms our answer.

Why Other Options Are Wrong:

• Option 960: This equals 240 * 4 and ignores the increasing multiplier pattern.
• Option 1080: This is 240 * 4.5, which does not follow integer multipliers.
• Option 1920: This is 240 * 8, which skips the planned multiplier 6.
• Option 720: This is 240 * 3 and would move backwards in the pattern of increasing multipliers.

Common Pitfalls:
Some students focus on differences instead of ratios, which do not give a simple pattern for this kind of series because the differences grow faster than linearly. Others may miscalculate the multipliers or fail to notice that they form the sequence 2, 3, 4, 5. Always consider both differences and ratios in multiplicative series, and double check your arithmetic when working with larger numbers.

Final Answer:
The next term in the series is 1440.