Sequences

Summary and Exam Tips for Sequences

Sequences is a subtopic of Sequences, Functions, and Graphs, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This topic covers various types of sequences, including linear, quadratic, cubic, arithmetic, and geometric sequences. Understanding sequences involves describing the rule for continuing a sequence and using the nth term to find specific terms. For linear sequences, the difference method helps determine the general term, such as $Un = 4n - 2$. Quadratic sequences require calculating the first and second differences to find the nth term, like $n^2 + 2n - 1$. Cubic sequences involve finding the third difference to derive expressions like $n^3 + 2n^2 - n + 2$. In geometric sequences, each term is obtained by multiplying the previous term by a constant, known as the common ratio. Arithmetic sequences use a fixed quantity, called the common difference, to generate terms. The sum of terms in a sequence is referred to as a series. Mastery of these concepts is crucial for solving sequence-related problems effectively.

Exam Tips

• Understand the Basics: Ensure you can describe the rule for continuing a sequence and use the nth term to find specific terms.
• Practice the Difference Method: For linear, quadratic, and cubic sequences, practice using the difference method to find the general term.
• Memorize Key Formulas: Know the formulas for the nth term of arithmetic and geometric sequences, as well as how to calculate the sum of a series.
• Solve Practice Questions: Regularly solve practice questions and past paper questions to familiarize yourself with different types of sequence problems.
• Check Your Work: Always double-check your calculations, especially when solving simultaneous equations for quadratic and cubic sequences.