A geometric series is the sum of a geometric sequence. That is,
where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence's start value.


To solve exercises using geometric sequences you need the following formulas:

• The nth term: a_n=a₁·r^n-1
• The sum of the first n terms:
  
  
• The sum of an infinite geometric serie: only if |r|<1.
  
  where:
  
  a₁ = the first term of the sequence
  r = common rate
  n = number of terms
  a_n = nth term
  S_n = sum of the first n terms
  S= sum of an infinite geometric serie

Given , find S₇
This is a geometric serie with a common rate r=3.