Geometric sequences

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  1. Geometric sequence formula
    Consider the geometric sequence: 2, 6, 18, 54, … .
    1. Identify the common ratio.
    2. Determine the sixth term of the sequence.
    3. Which term in the sequence has a value of 39366?
  2. Determine t1,r,tnt_1,r,t_n for the sequences in which two terms are given:
    t3=18 t_3=18, t6=486t_6=486
    1. Three consecutive terms of a geometric sequence are written in the form
      5(x+2),8x,x2 5(x+2),8-x,x-2
      Find the common ratio and the possible value of each of the three terms.
      Topic Notes
      A geometric sequence, also called geometric progression, is a number sequence with a common ratio between successive terms. A term in a geometric sequence can be found by multiplying the previous one by a non-zero and fixed number (a common ratio).
      • geometric sequence: a sequence with a common ratio between successive terms.
      • the nth term, tn{t_n} ,of a geometric sequence:
      tn  =  t1rn1{t_n}\; = \;{t_1} \cdot {r^{n - 1}}
      where, tn{t_n} : nth term
      t1{t_1} : first term
      r : common ratio
      Basic Concepts