Answer :
ANSWER
[tex]\text{The explicit formula of the sequence is a}_n\text{ = 12(}\frac{3}{2})^{n\text{ - 1}}[/tex]STEP-BY-STEP EXPLANATION:
Given the below sequence
12, 18, 27, 40.5, 60.75
From the sequence provided, you will see that the sequence is a geometric sequence
The next step is to find the common ratio
[tex]\text{common ratio= }\frac{next\text{ term}}{\text{previous term}}[/tex][tex]\begin{gathered} \text{Common ratio = }\frac{18}{12} \\ \text{common ratio = }\frac{3}{2} \\ \end{gathered}[/tex]Recall that, the nth term of a geometric progression is given as
[tex]a_n=ar^{n\text{ - 1}}[/tex]Where
a = first term
n = number of terms
r = common ratio
The next thing is to find the explicit formula
From the given sequence, the first term of the sequence is 12, and the common ratio of the sequence is 3/2
[tex]\begin{gathered} a_n\text{ = 12 }\times(\text{ }\frac{3}{2})^{n\text{ - 1}} \\ a_n\text{ = 12(}\frac{3}{2})^{n\text{ - 1}} \end{gathered}[/tex]