Geometric Sequences
Key Questions
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The common ratio of a geometric sequence, denoted by
#r# , is obtained by dividing a term by its preceding termconsidering the below geometric sequence:
#4 , 20 , 100# ...we can calculate
#r# as follows:
1)#20/4 = 5#
2)#100/20 = 5# so for the above mentioned geometric sequence the common ratio
# r = 5# 
Don't Memorise
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3
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May 18 2015
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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:
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#1, 2, 4, 8, \cdots# - the common ratio is 2. -
#-1, 3, -9, 27# - the common ratio is -3. -
#7,1, 1/7, 1/49# - the common ratio is 1/7.
Parth K. · · Sep 27 2014
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