Answer:
The formula is:
[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]
Step-by-step explanation:
The geometric sequences are those in which the division between the terms [tex]a_{n + 1}[/tex] and [tex]a_n[/tex] of the sequence are equal to a constant common reason called "r"
The geometrics secencias have the following form:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence
In this sequence we have the following terms
1.2, 3, 7.5, 18.75
Then notice that:
[tex]\frac{3}{1.2}=\frac{5}{2}\\\\\frac{7.5}{3}=\frac{5}{2}\\\\\frac{18.75}{7.5}=\frac{5}{2}[/tex]
Then:
[tex]r=\frac{5}{2}[/tex] and [tex]a_1=1.2[/tex]
Finally the formula is:
[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]
