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Sequences and Series

NIOS · Class 12 · Mathematics

Quick revision notes for Sequences and Series — NIOS Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

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
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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
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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
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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

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Full Notes

Key Concepts

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

Frequently Asked Questions

What are the important topics in Sequences and Series for NIOS Class 12 Mathematics?
Sequences and Series covers several key topics that are frequently asked in NIOS Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Sequences and Series — NIOS Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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