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