Answer:
[tex]a_n=48*1.5^{n-1}[/tex]
Step-by-step explanation:
Geometric Sequence
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:
[tex]r=\frac{72}{48}=1.5[/tex]
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:
[tex]a_n=a_1*r^{n-1}[/tex]
Where a1=48 and r=1.5
[tex]\boxed{a_n=48*1.5^{n-1}}[/tex]
For example, to find the 5th term:
[tex]a_5=48*1.5^{5-1}=48*1.5^{4}=243[/tex]
