Number sequences: mixed review

Key Notes :

Definition of Number Sequences

  • A number sequence is a set of numbers arranged in a specific order based on a rule or pattern.

Types of Number Sequences

  • Arithmetic Sequences: Numbers increase or decrease by the same amount (common difference).
    Example: 2, 4, 6, 8 (difference: +2).
  • Geometric Sequences: Numbers multiply or divide by the same factor (common ratio).
    Example: 3, 9, 27 (factor: ×3).
  • Fibonacci Sequence: Each number is the sum of the two preceding ones.
    Example: 0, 1, 1, 2, 3, 5.
  • Miscellaneous Patterns: May involve squares, cubes, primes, or other operations.

Identifying the Rule

  • Look for patterns like addition, subtraction, multiplication, division, or a combination of operations.
  • Check for alternating patterns or changes at specific intervals.

Examples of Mixed Patterns

  • Alternating operations: 2, 4, 8, 10, 20, 22 (×2, +2).
  • Increasing differences: 1, 3, 6, 10, 15 (difference increases by +1 each time).

Practice Questions

  • Complete the sequence: 5, 10, 20, 40, __, __ (Rule: ×2).
  • Find the missing number: 2, 6, __, 14, 18 (Rule: +4).

Common Mistakes

  • Not applying the rule consistently.
  • Assuming the wrong operation (e.g., adding instead of multiplying).

Learn with an example

1) Type the missing number in this sequence:

2,  _______,    50,    250,    1,250

First, look for a pattern. Notice how each number is 5 times the previous number:

2,    __,    50,    250,    1,250

Multiply 2 by 5 to find the missing number:

2 × 5 = 10

To make the pattern complete, the number 10 must go in the blank space.

2) Type the missing number in this sequence:

5,    25,   ______ ,    625,    3,125,    15,625

First, look for a pattern. Notice how each number is 5 times the previous number:

5,    25,    __,    625,    3,125,    15,625

Multiply 25 by 5 to find the missing number:

25 × 5 = 125

To make the pattern complete, the number 125 must go in the blank space.

3) Type the missing number in this sequence:

4,    16,   ______ ,    256,    1,024

First, look for a pattern. Notice how each number is 4 times the previous number:

4,    16,    __,    256,    1,024

Multiply 16 by 4 to find the missing number:

16 × 4 = 64

To make the pattern complete, the number 64 must go in the blank space.

Let’s practice!🖊️