Revision Notes Class 10 Maths Ch 5 Arithmetic Progressions

A fast, one-glance recap of Class 10 Maths Chapter 5 (Arithmetic Progressions) — for full worked explanations, see the Solutions.

Revision Notes: Arithmetic Progressions

AP definition: a sequence where the difference between any two consecutive terms is constant (the common difference, d)
General form: a, a+d, a+2d, a+3d, …
nth term: aₙ = a + (n−1)d
nth term from the end (when last term l is known): treat l as first term with common difference −d
Sum of first n terms (when a, d known): Sₙ = (n/2)[2a + (n−1)d]
Sum of first n terms (when a, last term l known): Sₙ = (n/2)(a + l)
nth term from sums: aₙ = Sₙ − Sₙ−₁
Three consecutive AP terms are often taken as (a−d), a, (a+d) for easier algebra (sum = 3a)
Removed from current syllabus: Exercise 5.4 (optional exercise) is not part of the 2026-27 rationalised syllabus
Common exam traps: confusing “nth term” with “sum of n terms”; forgetting the (n−1) in aₙ; sign errors when d is negative