Number Series
What is Number Series?
A sequence of numbers such that the difference between the consecutive terms is constant (common difference). Example: 2, 4, 6, 8... (common difference is 2).
Key points
- To develop the ability to identify various patterns in number sequences.
- To accurately predict the next number or missing number based on the identified pattern.
- To improve speed and accuracy in solving number series questions.
Common exam trap
Assuming a simple pattern when a more complex one exists.
Definitions
- Term
Arithmetic Progression
- Meaning
A sequence of numbers such that the difference between the consecutive terms is constant (common difference). Example: 2, 4, 6, 8... (common difference is 2).
- Term
Geometric Progression
- Meaning
A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Example: 3, 6, 12, 24... (common ratio is 2).
- Term
Square Number
- Meaning
A number obtained by multiplying an integer by itself. Example: 9 is a square number (3*3).
- Term
Cube Number
- Meaning
A number obtained by multiplying an integer by itself three ×. Example: 27 is a cube number (3*3*3).
Learning objectives
To develop the ability to identify various patterns in number sequences.
To accurately predict the next number or missing number based on the identified pattern.
To improve speed and accuracy in solving number series questions.
Prerequisites
Basic arithmetic operations (addition, subtraction, multiplication, division).
Knowledge of squares and cubes up to 20-25.
Understanding of prime numbers and basic number theory concepts.
Common mistakes
Assuming a simple pattern when a more complex one exists.
Calculation errors while applying the identified pattern.
Not considering alternating or mixed operations.
Overthinking simple patterns.
Practice preview
What comes next in the sequence? 2, 5, 11, 23, 47, ?…
hard
What will come in place of the question mark (?) in the following number series? 2, 4, 6, 8, ?…
easy
What number should replace the question mark in the series? 1, 4, 9, 16, 25, ?…
medium