Progressions

Arithmetic progression

Keywords: Arithmetic progression

Arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For example: 1, 3, 5,.....,11,13,15,...

a 1 , a 2 , a 3 , . . . , a n 1 , a n , a n + 1 , . . .

n-th term of the sequence:

a n = a a + ( n 1 ) d
a n = a n 1 + a n + 1 2 ,     n > 1

The sum of the first n terms:

S n = a 1 + a n 2 n = [ 2 a 1 + ( n 1 ) d ] n 2