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Numbers and Sequences — Revision Notes

Tamil Nadu Board · Class 10 · Mathematics

Numbers and Sequences revision notes for Tamil Nadu Board Class 10 Mathematics: 4 topics in quick points. Includes Euclid's Division Lemma and Algorithm.

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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Key Topics to Revise

1

Euclid's Division Lemma and Algorithm

  • Euclid's Division Lemma: For any two positive integers a and b, there exist UNIQUE integers q and r such that a = bq + r, where 0 ≤ r < b.
  • Here a is the Dividend, b is the Divisor, q is the Quotient, and r is the Remainder.
  • The remainder r is ALWAYS less than the divisor b.
2

Fundamental Theorem of Arithmetic

  • Every positive integer greater than 1 can be expressed as a product of prime numbers in EXACTLY ONE WAY (apart from rearrangement of prime factors).
  • This unique representation is called the Prime Factorisation of the number.
  • N = p1^q1 × p2^q2 × p3^q3 × ... × pn^qn, where p1, p2,... are primes and q1, q2,... are natural numbers.
3

Modular Arithmetic (Congruence Modulo n)

  • Two integers a and b are congruent modulo n if their difference (a - b) is divisible by n. Written as: a ≡ b (mod n).
  • This means a and b leave the SAME REMAINDER when divided by n.
  • The number n is called the modulus.
4

Sequences – Definition and Types

  • A sequence is a real-valued function defined on the set of Natural Numbers (N) taking real values.
  • Each element in a sequence is called a TERM. The n-th term is denoted by a_n (or t_n).
  • A sequence is written as a1, a2, a3, ..., an, ...

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Full Notes

Key Concepts

For any two positive integersThis is a stepEvery positive integer greater than 1Two integers a and bIf a ≡ b (mod m)

Frequently Asked Questions

What are the important topics in Numbers and Sequences for Tamil Nadu Board Class 10 Mathematics?
Key topics in Numbers and Sequences include Euclid's Division Lemma and Algorithm, Fundamental Theorem of Arithmetic, Modular Arithmetic (Congruence Modulo n), Sequences – Definition and Types. Study these first, then practise questions on each for the Tamil Nadu Board Class 10 board exam.
How should I revise Numbers and Sequences for the Tamil Nadu Board Class 10 board exam?
Learn the core ideas first, then work through the 45 practice questions on Numbers and 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 Numbers and Sequences

All Tamil Nadu Board Class 10 Mathematics Revision Notes

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