Arithmetic Progressions

Welcome to AP Fundamentals

Learn the fundamental concepts of Arithmetic Progressions through interactive, step-by-step explanations. Each topic builds upon the previous one to ensure complete understanding.

What is an Arithmetic Progression?

Basic Definition

An Arithmetic Progression (AP) is a sequence of numbers where each term after the first is obtained by adding a fixed constant to the previous term.

Example: 2, 5, 8, 11, 14... (adding 3 each time)

General Form of AP

Standard Representation

Every arithmetic progression can be written in this general form:

a, a+d, a+2d, a+3d, a+4d, ...

where a = first term and d = common difference

Understanding Common Difference

Common Difference (d)

The common difference is the fixed value added to each term:

d = a₂ - a₁ = a₃ - a₂ = aₙ₊₁ - aₙ

Positive d

2, 5, 8, 11...

d = +3 (increasing)

Negative d

10, 7, 4, 1...

d = -3 (decreasing)

Zero d

5, 5, 5, 5...

d = 0 (constant)

General Term Formula

nth Term Formula

To find any term in an AP, use this formula:

aₙ = a + (n-1)d

where: a = first term, d = common difference, n = term position

Example: For AP 3, 7, 11, 15... (a=3, d=4)
5th term = 3 + (5-1)×4 = 3 + 16 = 19

Types of Arithmetic Progressions

Classification by Length

Finite AP

2, 5, 8, 11, 14

Limited terms with first and last

Infinite AP

1, 3, 5, 7, 9...

Continues forever

Try It Yourself

Check if sequence forms an AP

Enter four consecutive terms:

, , ,