Answer:
[tex]a_n=72 \cdot \left(-\dfrac16 \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_1 = 72 \implies a=72[/tex]
To calculate [tex]r[/tex], divide one term by its previous term:
[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{2}{-12}=-\dfrac16[/tex]
Therefore, [tex]a_n=72 \cdot \left(-\dfrac16 \right)^{n-1}[/tex]
