Number Series
What is Number Series?
A sequence of numbers such that the difference between the consecutive terms is constant.
Key formula / rule: Arithmetic Progression (Common Difference)
Key points
- Develop the ability to identify various patterns in number sequences.
- Enhance logical reasoning and analytical skills.
- Improve speed and accuracy in solving number series problems.
- Apply mathematical concepts to solve abstract problems.
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.
- 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.
- Term
Prime Number
- Meaning
A natural number greater than 1 that has no positive divisors other than 1 and itself.
- Term
Fibonacci Sequence
- Meaning
A sequence where each number is the sum of the two preceding ones, usually starting with 0 and 1.
Learning objectives
Develop the ability to identify various patterns in number sequences.
Enhance logical reasoning and analytical skills.
Improve speed and accuracy in solving number series problems.
Apply mathematical concepts to solve abstract problems.
Formulae
- Name
Arithmetic Progression (Common Difference)
- Note
The difference between consecutive terms is constant.
- Expression
a, a+d, a+2d, ...
- Name
Geometric Progression (Common Ratio)
- Note
The ratio between consecutive terms is constant.
- Expression
a, ar, ar2, ...
- Name
Square Numbers
- Note
1, 4, 9, 16, 25, ...
- Expression
n2
- Name
Cube Numbers
- Note
1, 8, 27, 64, 125, ...
- Expression
n3
- Name
Fibonacci Sequence
- Note
Starting with 0 and 1, each subsequent number is the sum of the two preceding ones.
- Expression
F(n) = F(n-1) + F(n-2)
Prerequisites
Basic arithmetic operations (addition, subtraction, multiplication, division).
Understanding of squares and cubes of numbers.
Knowledge of prime numbers and basic number theory.
Familiarity with arithmetic and geometric progressions.
Common mistakes
Assuming a simple pattern when a more complex one exists.
Calculation errors in identifying differences or ratios.
Not considering alternating patterns or combinations of operations.
Overlooking the possibility of squares, cubes, or prime numbers.
Keywords
Number Series
Logical Reasoning
Pattern Recognition
Arithmetic Progression
Geometric Progression
Squares
Cubes
Prime Numbers
Fibonacci
SSC CGL
Aptitude Test
Practice preview
What is the next number in the following series: 2, 5, 10, 17, 26, ?…
easy
Find the next number in the series: 1, 8, 27, 64, 125, ?…
medium
What is the next number in the series: 4, 10, 22, 46, 94, ?…
hard