Answer:
Formula for the geometric sequence is:
[tex]a_n=32\times (\frac{1}{4})^{n-1}\\[/tex]
Step-by-step explanation:
Given geometric sequence:
[tex]32,8,2,\frac{1}{2},..........n[/tex]
The formula for a geometric sequence to find the [tex]n[/tex]th term is given by:
[tex]a_n=a_1\times r^{n-1}\\[/tex]
Where [tex]a_n[/tex] represents the [tex]n[/tex]th term, [tex]a_1[/tex] represents first term and [tex]r[/tex] represents the common ratio between consecutive terms.
For the given sequence,
[tex]a_1=32[/tex]
[tex]r=\frac{8}{32}=\frac{2}{8}=\frac{1}{4}[/tex]
So, the formula for the sequence can be written as:
[tex]a_n=32\times (\frac{1}{4})^{n-1}\\[/tex]
