Answer:
[tex]a_n=32 \cdot \left(\dfrac32 \right)^{n-1}[/tex]
Step-by-step explanation:
The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.
Geometric sequence formula: [tex]a_n=a r^{n-1}[/tex]
where [tex]a[/tex] is the start term and [tex]r[/tex] is the common ratio
Given [tex]a = 32[/tex]
To calculate [tex]r[/tex], divide one term by its previous term:
[tex]\implies r=\dfrac{a_4}{a_3}=\dfrac{108}{72}=\dfrac32[/tex]
Therefore, [tex]a_n=32 \cdot \left(\dfrac32 \right)^{n-1}[/tex]
