Arithmetic Progressions

An arithmetic progression is a sequence

An arithmetic progression is a sequence of numbers where each term (except the first) is obtained by adding a fixed number to the previous term. For e

The common difference is the fixed

The common difference is the fixed number that we add to each term to get the next term. It is calculated as d = a_{k+1} - a_k (the difference between

The first term 'a' is

The first term 'a' is the starting number of the AP. We denote terms as a_1 (first term), a_2 (second term), a_3 (third term), and a_n (nth term). To

This formula allows us to find

This formula allows us to find any term in the AP without listing all previous terms. For the nth term: we start with the first term 'a' and add (n-1)

To find the sum of

To find the sum of the first n terms of an AP, we use S_n = n/2[2a + (n-1)d], where n is the number of terms, a is the first term, and d is the common