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CMAT Topics

Sequence and Series

Sequence and Series form the foundation of number patterns in mathematics. They are widely used in TU CMAT to test logical thinking, pattern recognition, and numerical progression.

Practice MCQs for Sequence and Series

Fundamental Principles

Sequence

A sequence is an ordered list of numbers following a specific pattern.

Finite Sequence

A sequence with a limited number of terms is called a finite sequence.

Infinite Sequence

A sequence that continues indefinitely is called an infinite sequence.

Series

A series is the sum of the terms of a sequence.

Arithmetic Progression (AP)

A sequence in which the difference between consecutive terms is constant. Formula: a, a+d, a+2d, ...

Geometric Progression (GP)

A sequence in which each term is multiplied by a fixed ratio. Formula: a, ar, ar², ar³, ...

Harmonic Progression (HP)

A sequence whose reciprocals form an Arithmetic Progression.

Common Difference (d)

Difference between consecutive terms in AP.

Common Ratio (r)

Ratio between consecutive terms in GP.

Essential Formulation Tips

  • Identify pattern before solving sequence problems.
  • AP → look for difference, GP → look for ratio.
  • Convert HP problems into AP of reciprocals.
  • Write first few terms to understand pattern quickly.

Shortcut Execution Techniques

  • AP nth term: aₙ = a + (n-1)d
  • Sum of AP: Sₙ = n/2 [2a + (n-1)d]
  • GP nth term: aₙ = ar^(n-1)
  • Sum of GP: Sₙ = a(1 - rⁿ)/(1 - r)
  • Check difference or ratio quickly to identify AP or GP

Contextual Inquiries (FAQs)

Q: What is the difference between sequence and series?

A: A sequence is a list of numbers, while a series is the sum of those numbers.

Q: Which type of sequence is most important for CMAT?

A: Arithmetic Progression (AP) is most frequently tested in CMAT exams.

Q: How to identify AP or GP quickly?

A: Check if difference is constant (AP) or ratio is constant (GP).