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Syllabus

Sequences and Series — Syllabus

NIOS · Class 12 · Mathematics

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

45 questions25 flashcards2 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 Sequences and Series

1

1. Concept of Sequences

  • A sequence is a collection of numbers arranged in a definite order following a specific rule
  • Each number in a sequence is called a term, denoted as a₁, a₂, a₃, ..., aₙ
  • The nth term (general term) can be expressed as aₙ or tₙ
2

2. Arithmetic Progression (A.P.)

  • An A.P. is a sequence where the difference between consecutive terms is constant
  • This constant difference is called the common difference, denoted as 'd'
  • General form: a, a+d, a+2d, a+3d, ..., where 'a' is the first term
3

3. Arithmetic Mean (A.M.)

  • If three numbers a, A, b are in A.P., then A is the arithmetic mean between a and b
  • The arithmetic mean of two numbers is their average: A = (a + b)/2
  • Any number of arithmetic means can be inserted between two given numbers
4

4. Geometric Progression (G.P.)

  • A G.P. is a sequence where the ratio of consecutive terms is constant
  • This constant ratio is called the common ratio, denoted as 'r'
  • General form: a, ar, ar², ar³, ..., where 'a' is the first term and r ≠ 0, r ≠ 1

Key Concepts

A sequence is an ordered collectionAnThe common difference (d) isThis formula allows finding the nthThis formula calculates the sum

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Frequently Asked Questions

What are the important topics in Sequences and Series for NIOS Class 12 Mathematics?
Key topics in Sequences and Series include Concept of Sequences, Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.). Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Sequences and Series for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Sequences and Series. 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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