Answer:
[tex]a_{n}=-5(-3)^{n-1}[/tex]
Step-by-step explanation:
A geometric sequence or progession is defined as a sequence where each term can be found by multiplying a factor with the first term.
In this case, the first term is -5, the second term is 15 and the third term is -45.
[tex]a_{1}=-5\\a_{2}=15\\a_{3}=-45[/tex]
To find the factor, we divide the second term by the first, and the third term by the second.
[tex]\frac{15}{-5}=-3[/tex]
[tex]\frac{-45}{15}=-3[/tex]
As you can notice, the factor is -3, so [tex]r=-3[/tex].
Now, the explicit formula of this sequence can be found with
[tex]a_{n}=a_{1}r^{n-1}[/tex]
Where [tex]n[/tex] refers to the n-th term.
Replacing values, we have
[tex]a_{n}=-5(-3)^{n-1}[/tex]
Therefore, the explicit formula of the geometric sequence is
[tex]a_{n}=-5(-3)^{n-1}[/tex]
Which can be used to find any other term in the sequence.
