11-Plus Mathematics: Number Sequences

Understanding Number Sequences

Number sequences are a fundamental aspect of mathematics that involves recognizing and extending patterns. In the context of the 11-plus examination, students are expected to identify rules and relationships within sequences of numbers.

Recognising Patterns

Students learn to recognize various types of sequences, which can include:

• Arithmetic Sequences: These sequences are formed by adding or subtracting the same number to each term. For example, in the sequence 2, 5, 8, 11, the common difference is 3.
• Geometric Sequences: These sequences involve multiplying or dividing by the same number. For instance, in the sequence 3, 6, 12, 24, each term is multiplied by 2.

Finding the Rule

To find the rule of a sequence, students must look for the relationship between consecutive terms. This can often be expressed algebraically. For example, in the arithmetic sequence mentioned earlier, the nth term can be expressed as:

Worked Example

Problem: Find the nth term of the sequence 2, 5, 8, 11.

Solution:

• The first term (a) is 2.
• The common difference (d) is 3.
• The nth term can be calculated using the formula: nth term = a + (n - 1) * d.
• Substituting the values: nth term = 2 + (n - 1) * 3.
• This simplifies to nth term = 3n - 1.

Identifying Specific Terms

Students are also tasked with finding specific terms within a sequence. For example, to find the 5th term of the sequence 2, 5, 8, 11:

Worked Example

Problem: What is the 5th term of the sequence 2, 5, 8, 11?

Solution:

• Using the formula derived earlier: 5th term = 3(5) - 1.
• This simplifies to 15 - 1 = 14.
• Thus, the 5th term is 14.

Conclusion

Mastering number sequences is crucial for success in the 11-plus mathematics exam. By understanding how to recognize patterns, find rules, and identify specific terms, students will enhance their problem-solving skills and mathematical reasoning.