Class 10 · Chapter 5

Arithmetic Progressions

Sequences where each term differs from the previous by a fixed common difference; formulas for the $n$ -th term and sum of the first $n$ terms.

Watch this chapter

Top CBSE tutorials for Arithmetic Progressions

Curated video coming soon. For now, open the freshest CBSE-focused YouTube results — Magnet Brains, LearnoHub, Physics Wallah & more.

Read the full chapter

Mathematics · Class 10 (2026-27)

Official NCERT PDF

Latest 2026-27 edition on ncert.nic.in

NCERT Book Portal

Browse every chapter of the latest book

CBSE Academic Portal

Official CBSE curriculum

Tip: NCERT updated the syllabus for 2026-27. The links above open the latest edition on the official portal — chapter titles and numbering may differ from the notes shown here.

Detailed theory

An Arithmetic Progression (AP) is a sequence where each term after the first is obtained by adding a fixed number

d

(the common difference) to the previous term. Standard form:

a, a+d, a+2d, a+3d, \ldots

. The first term is

a

Key concepts & formulas

a_n = a + (n-1)d

S_n = \tfrac{n}{2}[2a + (n-1)d] = \tfrac{n}{2}(a+l)

where

l

is the last term.

d = a_n - a_{n-1}

(constant for an AP).

For an odd count

n

, the middle term is

a_{(n+1)/2}

Sum of first

n

natural numbers

= n(n+1)/2

Sum of first

n

odd numbers

= n^2