Understanding Number Series and Finding the Next Term

This question asks us to find the next number in the given series: 2, 4, 7, 11, 16, ?.

To solve number series questions, we need to look for a pattern or a rule that connects the terms. This pattern can involve addition, subtraction, multiplication, division, or a combination of operations, often involving the position of the term or the preceding term.

Analyzing the Pattern in the Series

Let's examine the differences between consecutive terms in the series:

• Difference between the 2nd term (4) and the 1st term (2): $\text{4} - \text{2} = \text{2}$
• Difference between the 3rd term (7) and the 2nd term (4): $\text{7} - \text{4} = \text{3}$
• Difference between the 4th term (11) and the 3rd term (7): $\text{11} - \text{7} = \text{4}$
• Difference between the 5th term (16) and the 4th term (11): $\text{16} - \text{11} = \text{5}$

The sequence of differences is 2, 3, 4, 5. We can observe that the difference between consecutive terms is increasing by 1 each time. This suggests that the next difference in the series will be 6.

Calculating the Next Number in the Series

Following the pattern of differences, the next difference should be 6. To find the next number in the original series, we add this next difference to the last term of the series.

The last term in the series is 16.

The next difference is 6.

Therefore, the next number in the series = Last term + Next difference

Next number = $\text{16} + \text{6} = \text{22}$

So, the next number in the series 2, 4, 7, 11, 16, ? is 22.

Verification using a Table

We can represent the series and the differences in a table:

The table clearly shows the pattern in the differences (2, 3, 4, 5, 6), confirming that the next term is 22.

Conclusion

The pattern in the series is that the difference between consecutive terms increases by 1 each time. Applying this pattern, the next term after 16 is found by adding 6 to 16, which gives 22.

Revision Table: Key Concepts for Number Series

Additional Information: Types of Number Series Patterns

Number series problems can have various patterns. Some common types include:

• Arithmetic Series: Constant difference between terms (e.g., 3, 6, 9, 12...).
• Geometric Series: Constant ratio between terms (e.g., 2, 4, 8, 16...).
• Difference Series: The differences between terms form a pattern (as seen in this problem).
• Double Difference Series: The differences between the differences form a pattern.
• Squares or Cubes: Terms are related to squares or cubes of numbers (e.g., 1, 4, 9, 16...).
• Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 1, 1, 2, 3, 5, 8...).
• Mixed Series: A combination of two or more patterns.

Solving number series problems often requires careful observation and systematic testing of different potential patterns.