Trends
What is Trends?
A sequence of numbers, letters, or symbols arranged in a particular order according to a rule.
Key formula / rule: Arithmetic Progression (Common Difference)
Key points
- To develop the ability to identify logical patterns in sequences.
- To accurately predict the next term or find the missing term in a series.
- To enhance analytical and problem-solving skills related to sequential data.
- To improve speed and accuracy in solving series-based questions.
Common exam trap
Assuming a simple pattern too quickly without verifying it for the entire series.
Definitions
- Term
Series
- Meaning
A sequence of numbers, letters, or symbols arranged in a particular order according to a rule.
- Term
Pattern
- Meaning
The underlying rule or logic that governs the progression of elements in a series.
- Term
Arithmetic Progression
- Meaning
A sequence where the difference between any two successive members is constant.
- Term
Geometric Progression
- Meaning
A sequence 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.
Learning objectives
To develop the ability to identify logical patterns in sequences.
To accurately predict the next term or find the missing term in a series.
To enhance analytical and problem-solving skills related to sequential data.
To improve speed and accuracy in solving series-based questions.
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 Series
- Note
Terms are perfect squares (1, 4, 9, 16...).
- Expression
n2
- Name
Cube Series
- Note
Terms are perfect cubes (1, 8, 27, 64...).
- Expression
n3
- Name
Prime Number Series
- Note
Sequence of prime numbers.
- Expression
2, 3, 5, 7, 11, ...
- Name
Fibonacci Series
- Note
Each term is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5...).
- Expression
F(n) = F(n-1) + F(n-2)
Prerequisites
Basic arithmetic operations (addition, subtraction, multiplication, division).
Knowledge of squares, cubes, and prime numbers.
Understanding of alphabetical order and letter positions.
Common mistakes
Assuming a simple pattern too quickly without verifying it for the entire series.
Calculation errors in arithmetic operations.
Confusing similar-looking patterns (e.g., arithmetic vs. geometric).
Incorrectly recalling letter positions or their reverse order.
Overlooking alternating patterns or patterns involving two interleaved series.
Keywords
Series
Number Series
Alphabet Series
Pattern Recognition
Logical Reasoning
Sequence
Progression
SSC CGL Reasoning
SSC CGL Quant
Arithmetic Progression
Geometric Progression
Prime Numbers
Squares
Cubes
Practice preview
Which of the following is the correct order of atomic radii of alkali metals?…
easy
Which of the following elements has the highest ionization enthalpy?…
medium
The metallic character of elements in Group 1 (alkali metals) follows which trend?…
easy