🔢 Arithmetic Progression

A sequence that jumps by the same step every time. Change the start and the step and watch the pattern!

first term a 2

common difference d 3

which term n 6

nth term: aₙ = a + (n−1)d

Sum of first n: Sₙ = n/2 [2a+(n−1)d]

🧠 The Big Idea

An AP adds a fixed common difference d each step: a, a+d, a+2d, …
nth term: aₙ = a + (n−1)d. Sum of n terms: Sₙ = n/2 × [2a + (n−1)d] = n/2 × (first + last).
APs are everywhere — saving a fixed amount monthly, stacking rows of seats, ticking seconds. ⏱️