Answer:
![a_n=48*1.5^{n-1}](https://tex.z-dn.net/?f=a_n%3D48%2A1.5%5E%7Bn-1%7D)
Step-by-step explanation:
<u>Geometric Sequence</u>
In geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
48, 72, 108, ...
The common ratio is found by dividing the second term by the first term:
![r=\frac{72}{48}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B72%7D%7B48%7D%3D1.5)
To ensure this is a geometric sequence, we use the ratio just calculated to find the third term a3=72*1.5=108.
Now we are sure this is a geometric sequence, we use the general term formula:
![a_n=a_1*r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%2Ar%5E%7Bn-1%7D)
Where a1=48 and r=1.5
![\boxed{a_n=48*1.5^{n-1}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_n%3D48%2A1.5%5E%7Bn-1%7D%7D)
For example, to find the 5th term:
![a_5=48*1.5^{5-1}=48*1.5^{4}=243](https://tex.z-dn.net/?f=a_5%3D48%2A1.5%5E%7B5-1%7D%3D48%2A1.5%5E%7B4%7D%3D243)