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Sequences and Series

NCERT Class 11 Mathematics Chapter 8

Sequences and Series for Class 11 Maths and JEE: sequences, series, arithmetic and geometric progressions, and the relation between A.M. and G.M.

5 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 8 “Sequences and Series”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.7 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Sequences

    Sequences for Class 11 Maths and JEE: the general term a, finite and infinite sequences, recurrences and the Fibonacci sequence, with solved examples.

    NCERT Section 8.2 11 min read 3 solved examples 8 practice questions

  2. Series

    Series for Class 11 Maths and JEE: series vs sequence, finite and infinite series, the sum of a series and sigma notation, with solved examples.

    NCERT Section 8.3 10 min read 3 solved examples 7 practice questions

  3. Arithmetic progression

    Arithmetic progression formulas for JEE Main: the nth term, the sum of n terms, 1 + 2 + … + n and arithmetic means, with solved examples and practice.

    JEE only 14 min read 4 solved examples 8 practice questions

  4. Geometric progression

    The nth term ar, the sum of n terms, the sum to infinity and geometric means, with solved examples.

    NCERT Section 8.4 14 min read 6 solved examples 27 practice questions

  5. Relationship between A.M. and G.M.

    The A.M.–G.M. inequality A ≥ G, its proof, when A = G, and least values, with solved examples.

    NCERT Section 8.5 12 min read 4 solved examples 8 practice questions

Key formulas in this chapter

Sequences

  • a = nth term (general term), n = 1, 2, 3, …
  • even numbers: a = 2n; odd numbers: a = 2n − 1
  • Fibonacci: a = a = 1, a = a + a for n > 2

Series

  • ∑ a (k = 1 to n) = a + a + … + a
  • ∑ (a + b) = ∑ a + ∑ b
  • ∑ c a = c ∑ a
  • ∑ c = nc (k = 1 to n)
  • k = m to n: n − m + 1 terms (integers m ≤ n)

Arithmetic progression

  • a = a + (n − 1)d
  • S = (n/2)(a + l) = (n/2)[2a + (n − 1)d]
  • 1 + 2 + 3 + … + n = n(n + 1)/2
  • A = (a + b)/2
  • d = (b − a)/(n + 1), A = a + kd
  • a = S − S (n ≥ 2), a = S

Geometric progression

  • a = ar
  • S = a(1 − r) / (1 − r) = a(r − 1) / (r − 1), r ≠ 1
  • S = na, r = 1
  • G = √(ab)
  • r = (b/a)1/(n+1)
  • G = ar, k = 1, 2, …, n
  • sum to infinity = a / (1 − r), −1 < r < 1

A.M. and G.M.

  • A = (a + b)/2, G = √(ab)
  • A − G = (√a − √b) / 2 ≥ 0
  • A ≥ G; A = G only when a = b
  • x − 2Ax + G = 0
  • a, b = A ± √(A − G)

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