Geometric Sequences

Key Questions

  • How do I find the common ratio of a geometric sequence?

    The common ratio of a geometric sequence, denoted by rr , is obtained by dividing a term by its preceding term

    considering the below geometric sequence:
    4 , 20 , 1004,20,100 ...

    we can calculate rr as follows:
    1) 20/4 = 5204=5
    2) 100/20 = 510020=5

    so for the above mentioned geometric sequence the common ratio r = 5r=5

    Don't Memorise · 3 · May 18 2015
  • How can I recognize a geometric sequence?

    That lies in its very definition: there is a common ratio between successive terms of the geometric sequence. That is to say, a number is being multiplied to get each successive term, and this "number" is nothing but the common ratio. This means that you just have to check if there is a number being multiplied between successive terms.

    If you also think about it, the common ratio is what you get when you divide a term by its predecessor. But you can probably already tell why you get the same number - it is because you have been multiplying the same number.

    The "common ratio" can be anything, but it has been widely argued without a proper consensus that a sequence with a common ratio 0 or 1 should not be called geometric. But thinking about that argument is futile, as you would never, ever encounter a sequence such as that in questions. Even if you do, you can think for yourself.

    Here are three examples:

    • 1, 2, 4, 8, \cdots1,2,4,8,⋯ - the common ratio is 2.

    • -1, 3, -9, 27−1,3,−9,27 - the common ratio is -3.

    • 7,1, 1/7, 1/497,1,17,149 - the common ratio is 1/7.

    Parth K. · · Sep 27 2014

Questions

Sequences