ANSWER
The explicit formula is
[tex]a_n= \frac{3}{2} ({ \frac{1}{2} })^{n - 1} [/tex]
EXPLANATION
The given geometric sequence is
[tex] \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32} [/tex]
The explicit formula is given by,
[tex]a_n = a_1 ({r})^{n - 1} [/tex]
where the first term is
[tex]a_1 = \frac{3}{2} [/tex]
and the common ratio is
[tex]r = \frac{a_2}{a_1} [/tex]
[tex]r = \frac{ \frac{3}{4} }{ \frac{3}{2} } [/tex]
This implies that,
[tex]r = \frac{3}{4} \times \frac{2}{3} [/tex]
[tex]r = \frac{1}{2} [/tex]
We now substitute all these values in to the formula to obtain,
[tex]a_n= \frac{3}{2} ({ \frac{1}{2} })^{n - 1} [/tex]
