Answer:
4, 2, 1, [tex]\frac{1}{2}[/tex].......
Step-by-step explanation:
Since explicit formula of a geometric sequence is represented by An = [tex]A_{1}(r)^{n-1}[/tex]
It is given in the question that fifth term of the sequence is [tex](\frac{1}{4})[/tex] and common ratio of the sequence is [tex]\frac{1}{2}[/tex].
Now from the explicit formula
[tex]A_{5}=\frac{1}{4} =A_{1}(\frac{1}{2})^{5-1}[/tex]
[tex]\frac{1}{4}=A_{1}( \frac{1}{2})^{4}[/tex]
[tex]A_{1} \frac{2^{4} }{4}[/tex]
[tex]\frac{16}{4}[/tex] = 4
Therefore, sequence will be 4, 4 × [tex](\frac{1}{2})[/tex], 4 × [tex]\frac{1}{2}^{2}[/tex], 4 × [tex](\frac{1}{2})[/tex]³.........
= 4, 2, 1, [tex]\frac{1}{2}[/tex].......
