# Week 2 : Geometric Sequence

Geometric Sequences
In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Example : 2,6,18,54, 163,486,1458,…

This sequence has a factor of 2 between each number

Each term is found by multiplying the previous term by 3 ( except the first term : 2 )

Infinite Gemetric Series :

In Infinite Geoemtric Series, when : r>1 or r<-1 it will be converges Let's see my example, and see what happends : 1,1/3,1/9,1/27,.. We have: a = 1 (the first term) r = 1/3 (halves each time) And so use this formula : $S_ \infty$ $S_ \infty$=1/1-1/3 $S_ \infty$=2/3 (0,666666..)