A geometric sequence is a sequence of numbers each of which, after the first, is obtained by multiplying the preceding number a constant number called the common ratio.. Thus, 3, 6, 12, 24, 48,... is a geometric sequence because each term is obtained by multiplying the preceding number by 2.

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

• The nth term:
• The sum of the first n terms:
  where:
  
  a₁ = the first term of the sequence
  r = common ratio
  n = number of terms
  a_n = nth term
  S = sum of the first n terms

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