Formula for geometric sequence for 32, eight, two, 1/2

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]