A geometric sequence is characterized by a common ratio.
The sequence is a geometric sequence
The sequence is given as:
18,9,9/2,9/4,9/8
Divide the second term by the first term to determine the common ratio (r)
[tex]r = 9 \div 18[/tex]
[tex]r = \frac 12[/tex]
Divide subsequent terms by the previous term;
If the result is the same as [tex]r = \frac 12[/tex], then the sequence is geometric
So, we have:
[tex]r =\frac 92 \div 9[/tex]
[tex]r = \frac 12[/tex]
[tex]r =\frac 94 \div \frac 92[/tex]
[tex]r = \frac 12[/tex]
[tex]r =\frac 98 \div \frac 94[/tex]
[tex]r = \frac 12[/tex]
Notice that the common ratio (r) is the same for all quotients.
Hence, the sequence is a geometric sequence
Read more about geometric sequence at:
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