Introduction to Sequence and Series for JEE Main

The chapter Sequence and Series is a key topic in Class 11 Maths, forming the foundation for algebra, calculus, and problem-solving in JEE Main.

A sequence is an ordered list of numbers, whereas a series is the sum of the terms of a sequence. Understanding AP, GP, and special series is essential for solving both conceptual and numerical problems efficiently.

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Arithmetic Progression (AP)

1. Definition:
   An Arithmetic Progression is a sequence in which the difference between consecutive terms is constant.

2. nth Term of AP:

• Tn = a + (n – 1)d, where a = first term, d = common difference

3. Sum of First n Terms of AP:

• Sn = n/2 × [2a + (n – 1)d]

• Alternative formula: Sn = n/2 × (a + l), where l = last term

4. Properties and Applications:

• AP is used in linear sequences, age problems, and consecutive numbers

• Solve problems involving sum of terms, finding middle term, or missing terms

Example: Find the 10th term of AP: 3, 7, 11, …

• T10 = 3 + (10 – 1)×4 = 39

Geometric Progression (GP)

1. Definition:
   A Geometric Progression is a sequence in which each term after the first is obtained by multiplying the previous term by a fixed number r (common ratio).

2. nth Term of GP:

• Tn = a × r^(n–1)

3. Sum of First n Terms of GP:

• Sn = a × (1 – r^n) / (1 – r), r ≠ 1

• Sum to Infinity (|r| < 1): S∞ = a / (1 – r)

4. Properties and Applications:

• GP is used in growth and decay problems, compound interest, and series summation

• Solve problems involving sum, nth term, or missing terms

Example: Sum of first 5 terms of GP: 2, 6, 18, …

• Sn = 2 × (1 – 3^5)/(1 – 3) = 242

Special Sequences and Series

1. Harmonic Progression (HP):

• Sequence where reciprocals form an AP

• nth term: Tn = 1 / [a + (n–1)d]

2. Relationship between AP, GP, and HP:

• Used in advanced problems involving combined sequences

• Frequently tested in JEE Main reasoning-based numerical questions

3. Sum of Special Series:

• Squares: 1² + 2² + … + n² = n(n + 1)(2n + 1)/6

• Cubes: 1³ + 2³ + … + n³ = [n(n + 1)/2]²

• Useful for shortcut calculations in exam

Applications of Sequence and Series in JEE Main

• Solve algebraic problems involving sums and terms

• Basis for arithmetic and geometric word problems

• Solve progression-based reasoning and logic questions

• Used in probability, calculus, and advanced number problems

Example: The sum of first 20 terms of an AP is 210. If the first term is 5, find the common difference.

Important JEE Main Preparation Tips for Sequence and Series

• Memorize formulas for nth term and sum of AP, GP, HP

• Practice solving problems with missing terms, middle terms, and sums

• Use shortcuts for sum of squares and cubes

• Solve previous year JEE Main MCQs and numerical problems

• Visualize relationships between different types of progressions

Why Study Sequence and Series from Studentbro.in?

Studentbro.in provides:

• Step-by-step explanations of AP, GP, HP, and special series

• Solved examples for nth term, sum, and series problems

• Charts, tables, and diagrams for quick revision

• MCQs and PYQs aligned with JEE Main syllabus

Conclusion

The Sequence and Series chapter is fundamental and scoring in Class 11 Maths for JEE Main. Mastery of AP, GP, HP, nth term, sum formulas, and special series helps students solve conceptual and numerical problems efficiently.

Studentbro.in provides structured, easy-to-understand, and exam-focused content to master Sequence and Series effectively and boost JEE Main scores.