Answer:
Option A - [tex]......,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
Step-by-step explanation:
Given : A geometric has [tex]\frac{1}{4}[/tex] as its's fifth term and [tex]\frac{1}{2}[/tex] as common ratio.
To find : Which sequence is geometric ?
Solution :
The geometric sequence is defined as [tex]a,ar,ar^2,ar^3...[/tex]
where, a is the first term and r is the common ratio.
The nth term of the sequence is [tex]a_n=ar^{n-1}[/tex]
We have given, [tex]r=\frac{1}{2}[/tex] and [tex]a_5=\frac{1}{4}[/tex]
The 5'th term is
[tex]a_5=ar^{5-1}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{2})^{4}[/tex]
[tex]\frac{1}{4}=a(\frac{1}{16})[/tex]
[tex]\frac{16}{4}=a[/tex]
[tex]a=4[/tex]
The sequence form is [tex]4,4(\frac{1}{2}),4(\frac{1}{2})^2,4(\frac{1}{2})^3,4(\frac{1}{2})^4,4(\frac{1}{2})^5...[/tex]
[tex]4,2,1,\frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]
From the given sequence Option A matched with result.
Therefore, Option A is correct.
