Answer:
The common ratio of the geometric sequence is:
[tex]r=-2[/tex]
Step-by-step explanation:
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
where
Given the sequence
[tex]-2,\:4,-8,\:16,\:-32,\:...[/tex]
Compute the ratios of all the adjacent terms: [tex]r=\frac{a_n+1}{a_n}[/tex]
[tex]\frac{4}{-2}=-2,\:\quad \frac{-8}{4}=-2,\:\quad \frac{16}{-8}=-2,\:\quad \frac{-32}{16}=-2[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=-2[/tex]
Therefore, the common ratio of the geometric sequence is:
