EDEXCEL GCSE FOUNDATION MATHS - What are Sequences

EDEXCEL GCSE Foundation Maths: What are Sequences?

A sequence is a list of numbers that follow a specific rule or pattern. Each number in the sequence is called a term.

Understanding Sequences:

• Arithmetic Sequences: In an arithmetic sequence, the difference between consecutive terms is always the same. This difference is called the common difference.

• Example: 2, 5, 8, 11, 14... (Common difference = 3)

• Geometric Sequences: In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio.

• Example: 3, 9, 27, 81, 243... (Common ratio = 3)

Finding the nth Term:

To find the nth term of a sequence, we need to identify the rule that generates the sequence. Here's how to do it:

1. Arithmetic Sequences:

• Rule: nth term = a + (n - 1)d

• Where:

  • a = the first term
  • d = the common difference
  • n = the position of the term in the sequence

• Example: Find the 10th term of the sequence 2, 5, 8, 11...

• a = 2
• d = 3
• n = 10
• 10th term = 2 + (10 - 1) * 3 = 29

2. Geometric Sequences:

• Rule: nth term = ar^(n-1)

• Where:

  • a = the first term
  • r = the common ratio
  • n = the position of the term in the sequence

• Example: Find the 6th term of the sequence 3, 9, 27, 81...

• a = 3
• r = 3
• n = 6
• 6th term = 3 * 3^(6-1) = 243

Key Points:

• Sequences can be either finite (ending) or infinite (continuing forever).
• You can find the missing terms in a sequence by applying the rule.
• Understanding sequences is essential for various mathematical concepts, including algebra, functions, and graphs.

Practice:

1. Identify whether the following sequences are arithmetic, geometric, or neither:
2. a) 1, 3, 5, 7, 9...
3. b) 2, 4, 8, 16, 32...
4. c) 1, 2, 4, 7, 11...
5. Find the 8th term of the sequence 4, 7, 10, 13...
6. Find the 5th term of the sequence 2, 6, 18, 54...

By practicing these concepts and applying the rules, you will be able to understand and analyze sequences effectively in your Edexcel GCSE Foundation Maths exam.