Chapter 8 — Sequences and Series

Chapter 8 of the Class 11 Maths NCERT textbook, "Sequences and Series", covers arithmetic and geometric progressions, their formulas for nth terms and sums, geometric means, and the relationship between arithmetic and geometric means.

• Patterns in ordered numbers — The chapter treats a sequence as an ordered list following a rule and singles out progressions — regular patterns — as the sequences worth studying, distinguishing finite from infinite ones along the way.
• Geometric progressions — Building on arithmetic progressions, it develops the geometric progression, where each term is a constant ratio of the previous one, and derives compact formulas for any term and for the sum of many terms.
• Means and real-world growth — Geometric means and the arithmetic-mean-versus-geometric-mean relationship close the chapter, with applications to population, deposits and depreciation showing how these sequences model multiplicative change in the real world.

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