Arithmetic Progression (AP)

In this lesson, we'll learn about arithmetic progression.

We'll cover the following

Arithmetic progression is a sequence of numbers such that the difference between each consecutive term is constant, commonly denoted by dd. For example:

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

Here, the first term, aa, is 33, a=3a=3, and the common difference, dd, is 22, d=2d=2. In general, AP is

a,a+d,a+2d,...,a+(n1)da, a+d , a+2d, ... , a+(n-1)d

where nthnth term an=a+(n1)da_{n} = a+(n-1)d


Sum

Sum of AP with nn terms is

a+(a+d)+(a+2d)+...+(a+(n1)d)a + (a+d) + (a+2d) + ... + (a+(n-1)d)

= na+d(1+2+3+...+n1)na + d(1 + 2 + 3 + ... + n-1)

= na+d(n(n1)2)na + d(\frac{n(n-1)}{2})

= n2[2a+d(n1)]\frac{n}{2}[2a + d(n-1)]


In the next lesson, we’ll learn about geometric progression.

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