Arithmetic Progressions

An AP is a sequence where

An AP is a sequence where each term (after the first) equals the previous term plus a constant value. Mathematically, if a₁, a₂, a₃, ... form an AP, t

The fixed constant added to each

The fixed constant added to each term to get the next term. Calculated as d = a_{k+1} - a_k for any consecutive terms. The common difference can be po

Any AP can be written as

Any AP can be written as: a, a+d, a+2d, a+3d, ... where 'a' is the first term and 'd' is the common difference. This form makes it clear that to find

This formula finds any term

This formula finds any term in an AP without listing all previous terms. Here, a_n is the nth term, 'a' is the first term, 'd' is the common differenc

This formula calculates the sum

This formula calculates the sum of the first n terms of an AP without adding each term individually. Alternative form: S_n = n/2(a + l) where l is the