We are given sequence -4.5 , -4 , -3.5, -3, -2.5 .
For the given sequance first term is -4.5 and if we check differences of next term to previous term, we get
-4-(-4.5) = 0.5
-3.5 - (-4) = 0.5
-3 -(-3.5) = 0.5.
-2.5 -(-3) = 0.5.
Each time the difference is same.
So, the given sequance is an Arithmetic sequence.
We can find the required function for the given sequnace by applying nth term of an Arithmetic sequence formula.
[tex]a_n= a_1+(n-1)*d[/tex]
Where, a1 is the first term, d is the common difference and n is the number of terms.
Plugging values of a1 and d in the above formula, we get
[tex]a_n=-4.5+(n-1)*0.5[/tex]
On simplifying, we get
[tex]a_n= -4.5+0.5n-0.5.[/tex]
[tex]a_n=-5.0+0.5n.[/tex]
In function form, we can write it as
f(n) = 0.5n -5.0.
