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Concept Maps

Some Special Sequences — Concept Maps

NIOS · Class 12 · Mathematics

3 concept maps of Some Special Sequences for NIOS Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards6 formulas & key relations5 concepts

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Illustrates the definition of a sequence as an ordered collection of objects, showing how terms are indexed by natural numbers and providing simple examples.
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3 Concept Maps

Overview of Some Special Sequences Chapter

Overview of Some Special Sequences Chapter

The map in words

  • Special Sequences
    • Series Basics
      • Definition
      • nth Term Formula
      • Finding tₙ from Pattern
      • Alternating Sign Series
    • Key Sum Formulas
      • Sum of n Natural Numbers
        • Formula: n times n+1 div 2
        • Derived from AP
      • Sum of Squares
        • Formula: n times n+1 times 2n+1 div 6
        • Derived by Telescoping
      • Sum of Cubes
        • Formula: Square of n times n+1 div 2
        • Equals Square of Sum
    • Product Series
      • Two Factor Products
        • Example: 1.3 plus 3.5 plus 5.7
        • Expand tₙ then Sum
      • Three Factor Products
        • Example: 2.3.5 plus 3.5.7
        • Expand Fully then Sum
    • Fraction Series
      • Partial Fractions Method
      • Telescoping Cancellation
      • Example: 1 over 1.3 plus 1 over 3.5
    • Derivation Methods
      • Method of Differences
      • Telescoping Sums
      • Mathematical Induction

Mind map showing the relationship between sequences and series, including their types and characteristics

Mind map showing the relationship between sequences and series, including their types and characteristics

The map in words

  • Sequences and Series
    • Sequence
      • Definition
      • Ordered list
      • Definite pattern
      • nth term formula
    • Series
      • Sum of terms
      • Finite series
      • Infinite series
      • Summation notation
    • Types
      • Arithmetic
      • Geometric
      • Special sequences

Flowchart showing the step-by-step process of finding terms in a sequence using the nth term formula

Flowchart showing the step-by-step process of finding terms in a sequence using the nth term formula

The map in words

  • Given: nth term formula Tₙ
    • Substitute n = 1
      • Calculate T₁
        • Write sequence
          • Identify pattern
            • Form series by addition
    • Substitute n = 2
      • Calculate T₂
    • Substitute n = 3
      • Calculate T₃

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Frequently Asked Questions

What are the important topics in Some Special Sequences for NIOS Class 12 Mathematics?
Key topics in Some Special Sequences include What is a Series?, The Three Master Formulas — Σn, Σn², Σn³, Finding Sum of Special Series — Step-by-Step Method, Proof of Standard Formulas Using Method of Differences. Study these first, then practise questions on each for the NIOS Class 12 board exam.
What do the concept maps for Some Special Sequences show?
The 3 maps show how the ideas in Some Special Sequences connect: Overview of Some Special Sequences Chapter; Mind map showing the relationship between sequences and series, including their types and characteristics. Each map is also written out as an outline on this page.
How should I revise Some Special Sequences for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Some Special Sequences. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Some Special Sequences

All NIOS Class 12 Mathematics Concept Maps

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