9.3 Geometric Sequences

• In a Geometric sequence, each term is found by multiplying the previous term by a constant, and the it is common ratio(r). 

          Example:  1, 2, 4, 8.....
                          The sequence starts at 1 and next term will doubled for each time
                           so we would know that r =2/1=2
          Also, when r=0, then it is not geometric.

• The nth term of a geometric sequence

           a_n = a₁ r^{n-1
           Example: 10, 30, 90, 270....
                           the 4th term would be: a}₄ = 10×3^(4-1) = 10×3³ = 10×27 = 270

•  The sum of a finite geometric sequence

• The sum of an infinite geometric sequence