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What is an example of a number pattern for Grade 8?

Published in Number Patterns 2 mins read

Here are examples of number patterns suitable for Grade 8, drawn from the provided sequences. These sequences illustrate different types of patterns, from simple arithmetic to geometric and more complex patterns.

Examples of Number Patterns for Grade 8

Below are several examples of number patterns, explained for Grade 8 students.

Arithmetic Sequences

Arithmetic sequences are number patterns where the difference between consecutive terms is constant.

  • Sequence A: 2; 5; 8; 11; 14; 17; 20; 23;

    • Here, the common difference is 3. Each number is 3 more than the previous one (e.g., 5-2=3, 8-5=3, 11-8=3). This can be expressed as a_n = 2 + 3(n-1), where a_n is the nth term in the sequence.

  • Sequence G: 1; 5; 9; 13; 17; 21; 25; 29; 33;

    • The common difference is 4. Each number is 4 more than the one before it (e.g., 5-1=4, 9-5=4, 13-9=4). This sequence can be defined as a_n = 1 + 4(n-1).

Geometric Sequences

Geometric sequences involve a constant ratio between consecutive terms.

  • Sequence C: 1; 2; 4; 8; 16; 32; 64;
    • Here, the common ratio is 2. Each number is twice the previous one (e.g., 2/1=2, 4/2=2, 8/4=2). The rule for this is a_n = 1 * 2^(n-1).
  • Sequence H: 2; 4; 8; 16; 32; 64;
    • The common ratio is 2. Each number is double the one before (e.g., 4/2=2, 8/4=2, 16/8=2). The formula is a_n = 2 * 2^(n-1) which is also a_n = 2^n.
  • Sequence F: 2; 6; 18; 54; 162; 486;
    • The common ratio is 3. Each number is three times the previous one (e.g., 6/2=3, 18/6=3, 54/18=3). This can be shown as a_n = 2 * 3^(n-1).

Sequences with More Complex Patterns

These patterns involve differences that are not constant.

  • Sequence B: 4; 5; 8; 13; 20; 29; 40;
    • The differences between terms are 1, 3, 5, 7, 9, 11... which is a pattern of adding consecutive odd numbers.
  • Sequence E: 4; 5; 7; 10; 14; 19; 25; 32; 40;
    • The differences between terms are 1, 2, 3, 4, 5, 6, 7, 8... which is a pattern of adding consecutive natural numbers.

Understanding Number Patterns

  • Analyzing the differences: Look at the difference between consecutive numbers. If it's constant, it's arithmetic.
  • Checking the ratio: If the ratio between consecutive numbers is constant, it's geometric.
  • Finding the rule: Determine the underlying rule or formula that generates the sequence to find any term.

These examples demonstrate various number patterns that are appropriate for Grade 8 mathematics.

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