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Some Special Sequences — Syllabus

NIOS · Class 12 · Mathematics

What Some Special Sequences covers in NIOS Class 12 Mathematics: 4 topics, for the 2026-27 session. Part of the NIOS Class 12 Mathematics syllabus.

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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4 Topics · NIOS Class 12 Mathematics · 2026-27

Topics in Some Special Sequences

1

What is a Series?

  • A sequence is an ordered list of numbers following a definite rule, e.g., 1, 4, 9, 16, ...
  • A series is formed by adding the terms of a sequence: 1 + 4 + 9 + 16 + ...
  • Every sequence has a corresponding series associated with it.
2

The Three Master Formulas — Σn, Σn², Σn³

  • These three formulas are the backbone of this entire chapter. Memorise them perfectly.
  • Σn = sum of first n natural numbers = n(n+1)/2
  • Σn² = sum of squares of first n natural numbers = n(n+1)(2n+1)/6
3

Finding Sum of Special Series — Step-by-Step Method

  • The METHOD for ALL series sum problems is the same — always follow these 4 steps.
  • STEP 1: Find tₙ — identify the nth term of the series by observing the pattern.
  • STEP 2: Express tₙ as a polynomial in n — expand any products completely.
4

Proof of Standard Formulas Using Method of Differences

  • The method of differences (telescoping) is used to DERIVE the standard sum formulas.
  • For Σn²: Use the identity n³ - (n-1)³ = 3n² - 3n + 1. Write this for n = 1, 2, 3, ..., n and add.
  • For Σn³: Use the identity n⁴ - (n-1)⁴ = 4n³ - 6n² + 4n - 1. Write this for n = 1, 2, ..., n and add.

Key Concepts

A series is an expressionThe nth termThe series 1 + 2 +The series 1² + 2² +The series 1³ + 2³ +

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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.
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.

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