Class 11 Maths Chapter 8 Sequences and Series – Revision Notes

Class 11 Maths Chapter 8 draws a line between two patterns: arithmetic progressions, where terms grow by a fixed amount, and geometric progressions, where they grow by a fixed multiple. Below are the nth-term and sum formulas for both, along with the special series used to sum squares and cubes.

Last Updated: September 23, 2026

AP (Recap)

• a_n=a+(n−1)d; S_n=n/2[2a+(n−1)d].

GP

• Common ratio r; a_n=arⁿ⁻¹.
• S_n=a(rⁿ−1)/(r−1), r≠1.
• Infinite GP (|r|<1): S∞=a/(1−r).

Means

• AM=(a+b)/2; GM=√(ab); AM≥GM (positive numbers).

Special Series

• ∑n = n(n+1)/2.
• ∑n² = n(n+1)(2n+1)/6.
• ∑n³ = [n(n+1)/2]².

One-Line Summary

Sequences follow AP (constant difference) or GP (constant ratio) patterns, with distinct nth-term and sum formulas, and an infinite GP converges to a finite sum only when |r|<1.

Frequently Asked Questions

What is the difference between a sequence and a series?
A sequence is an ordered list of numbers following a pattern, such as an arithmetic progression, while a series is the sum of the terms of a sequence.

How is a geometric progression different from an arithmetic progression?
In an arithmetic progression, consecutive terms differ by a constant common difference through addition, whereas in a geometric progression, consecutive terms have a constant common ratio through multiplication, leading to different sum formulas.

Written by Satish

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