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).
Example Breakdown: Arithmetic Sequence
Basic AP questionFirst term a = 2
Common difference d = 3
aₙ = a + (n-1)d
a₁₀ = 2 + 9×3 = 29
Example Breakdown: Sum of AP
Frequently asked CMAT questiona = 1, d = 2, n = 5
Sₙ = n/2 [2a + (n-1)d]
S₅ = 5/2 [2 + 8] = 25
Example Breakdown: Geometric Progression
Basic GP problema = 3, r = 2
aₙ = ar^(n-1)
a₅ = 3 × 2⁴ = 48
Example Breakdown: Sequence Pattern
Simple GP recognitionPattern is ×2 each time
Next term = 32
Sequence & Series Set 1: Basic AP Identification
Identify arithmetic patterns and basic sequence continuation.
Q1. Find next term: 4, 8, 12, 16, ?
Q2. Find common difference in 7, 10, 13, 16
Q3. Find 5th term of AP: 2, 5, 8, 11...
Q4. Which is an AP?
Q5. Next term: 10, 20, 30, ?
Q6. Find 3rd term of AP: 1, 4, 7, 10...
Q7. Sum of first 3 terms: 2, 4, 6
Q8. Find missing term: 5, ?, 15
Q9. Which is NOT AP?
Q10. Next term: 100, 90, 80, ?