Answer:The explicit rule for this sequence:
[tex]a_n=a_1(r)^{n-1}=3(\frac{1}{2})^{n-1}[/tex]
Step-by-step explanation:
[tex]a_1=3[/tex]
[tex]a_n=\frac{1}{2}a_{n-1}[/tex]
Where [tex]a_n[/tex] = n'th term in a sequence
[tex]a_2=\frac{1}{2}a_{(2-1)}=\frac{1}{2}a_1=\frac{1}{2}\times 3=\frac{3}{2}[/tex]
The value 'r' is geometric mean is given as:
r = common ratio
[tex]r=\frac{a_2}{a_1}=\frac{\frac{3}{2}}{3}=\frac{1}{2}[/tex]
The explicit rule for this sequence:
[tex]a_n=a_1(r)^{n-1}=3(\frac{1}{2})^{n-1}[/tex]
