Chapter 8 — Sequences and Series

NCERT Class 11 Mathematics Chapter 8 covers sequences and series, including arithmetic progressions, geometric progressions, and their formulas for nth terms and sums. The chapter also teaches geometric means and the relationship between arithmetic and geometric means.

Chapter 8 introduces sequences as ordered collections with identified first, second, and subsequent terms, and explains how sequences follow specific patterns called progressions. The chapter builds on previous arithmetic progression knowledge, then develops geometric progressions where each term bears a constant ratio to the preceding term. Key topics include: finding nth terms using formulas like an = arn–1 for geometric progressions, calculating sums using Sn = a(rn–1)/(r–1), geometric means of positive numbers, and the fundamental relationship A ≥ G between arithmetic and geometric means. Real-world applications span population dynamics, bank deposits, and commodity depreciation.

1. 01A sequence is an ordered collection of numbers with an identified position for each term; finite sequences have fixed terms, infinite sequences never end
2. 02Geometric progression (G.P.) is defined when the ratio of any term to its preceding term is constant (r), written as a, ar, ar², ar³, ...
3. 03The nth term of a G.P. is an = ar^(n–1); sum of first n terms is Sn = a(rn–1)/(r–1) when r ≠ 1, or Sn = na when r = 1
4. 04Geometric mean (G.M.) of two positive numbers a and b is √(ab), and any two positive numbers can have multiple geometric means inserted between them
5. 05Relationship between arithmetic mean (A.M.) and geometric mean: A ≥ G, with equality only when a = b