# Sequences and Series Notes, Class 11 Mathematics | SwaVid Sequences and Series, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/sequences-and-series Source: https://www.swavid.com/cbse/class-11/maths/chapter/sequences-and-series # Sequences and Series ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Sequences and series ### Geometric progression ### General term of a G.P. ### Sum of n terms of a G.P. ### Geometric mean ### Relationship between A.M. and G.M. ### Next chapter ### Related chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Sequences and Series Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 8. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter introduces sequences, series, and the detailed properties of geometric progressions. Students learn to find the general term, sum of n terms, geometric mean, and the relationship between arithmetic and geometric means. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 8, Sequences and Series A sequence is an ordered arrangement of numbers according to a definite rule. A series is the algebraic sum of the terms of a sequence. A sequence is called a geometric progression (G.P.) if the ratio of any term to its preceding term is always constant. This constant ratio is denoted by r, and the first term is denoted by a. The nth term of a geometric progression with first term a and common ratio r is given by aₙ = a rⁿ⁻¹. The sum Sₙ of the first n terms of a G.P. depends on the value of r. If r = 1, Sₙ = n a; if r ≠ 1, Sₙ = a (1 - rⁿ) / (1 - r) or Sₙ = a (rⁿ - 1) / (r - 1). The geometric mean (G.M.) of two positive numbers a and b is given by √(a b). Any number of geometric means can be inserted between two positive numbers such that the resulting sequence forms a G.P. For any two positive real numbers a and b, the arithmetic mean A = (a + b) / 2 and geometric mean G = √(a b) satisfy the inequality A ≥ G. Try each question first. Then tap it to see the answer. Identify first term a = 5 and common ratio r = 25 / 5 = 5. Use the formula for the nth term: a₁₀ = a r¹⁰⁻¹ = 5 × 5⁹. Compute a₁₀ = 5¹⁰ = 9765625. 9765625 Identify a = 1 and r = (2/3) / 1 = 2/3. Since r < 1, use S₅ = a (1 - r⁵) / (1 - r). Substitute values: S₅ = 1 × (1 - (2/3)⁵) / (1 - 2/3) = (1 - 32/243) / (1/3). Simplify: S₅ = (211/243) × 3 = 211 / 81. 211 / 81 Let G₁ and G₂ be the two numbers. The sequence 3, G₁, G₂, 81 forms a G.P. with a = 3 and n = 4 terms. Set the fourth term: a₄ = a r³ = 3 r³ = 81. Solve for r: r³ = 27, so r = 3. Calculate the terms: G₁ = 3 × 3 = 9, and G₂ = 9 × 3 = 27. 9 and 27 Straight Lines . Binomial Theorem . Relations and Functions . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Straight Lines. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 8 NCERT book - 80 marks, theory paper - 3 quick checks - Using rⁿ instead of rⁿ⁻¹ in the general term formula . Remember that the first term corresponds to n = 1, so the power of r is 1 - 1 = 0. The correct nth term is a rⁿ⁻¹. - Applying the G.M. formula to negative numbers . Geometric mean is strictly defined for positive real numbers in NCERT. Check that both numbers are positive before taking the square root. - Confusing the number of inserted means with total terms . When inserting n geometric means between a and b, the total number of terms in the resulting G.P. is n + 2, with b as the (n + 2)th term. ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/binomial-theorem) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/relations-and-functions) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)