Sequences

Summary and Exam Tips for Sequences

Sequences is a subtopic of Algebra, which falls under the subject Mathematics in the Cambridge Lower Secondary curriculum. A sequence is a list of numbers or objects arranged in a specific order. For example, the sequence 3, 5, 7, 9, ... starts at 3 and increases by 2 each time. There are two main rules to understand sequences: the term-to-term rule and the position-to-term rule. The term-to-term rule helps you find the next number in a sequence if you know the previous term(s). For instance, in the sequence 1, 3, 5, 7, ..., you add 2 to the previous term to find the next one. The position-to-term rule allows you to compute the value of any term directly. For example, in the sequence 1, 3, 5, 7, ..., the nth term is given by $a_n = 2n - 1$. An arithmetic sequence is a type of sequence where the same value, known as the common difference, is added each time. For example, in the sequence 1, 4, 7, 10, ..., the common difference is 3.

Exam Tips

• Understand the Rules: Make sure you are clear on both the term-to-term and position-to-term rules. Practice applying these rules to different sequences.
• Identify the Common Difference: For arithmetic sequences, quickly identify the common difference as it is crucial for solving problems.
• Practice with Examples: Work through various examples to become comfortable with identifying patterns and calculating terms.
• Use Formulas: Familiarize yourself with the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n-1) \cdot d$, where $d$ is the common difference.
• Check Your Work: Always double-check your calculations to ensure accuracy, especially in exams where small errors can lead to incorrect answers.