Geometric sequences

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/5
?
Examples
Lessons
  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
      ?