Progressions

Geometric progression

Keywords: Geometric progression

Geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
For example: 1, 2, 4,.....,32,64,128,...

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

n-th term of the sequence:

a n = a 1 q n 1
| a n | = a n 1 a n + 1 ,     n > 1

The sum of the first n terms:

S n = a 1 q n 1 q 1 ,     q 1