Respuesta :
Answer:
Recursive Formula: f(n) = f(n-1) - 30
[tex]\text{Explicit Formula: T}_n=\text{ 90-30n}[/tex]Explanations:In a recursive equation, a term is written in terms of the preceding term.
In the sequence 60, 30, 0, -30......
The common difference is (30 - 60) = -30
Which means that a term is written as a function of the preceding term.
If the current term is f(n)
The preceding term is f(n-1)
The number of terms is n
The recursive equation is then:
f(n) = f(n-1) - 30
For the explicit equation:
The sequence 60, 30, 0, -30..... is an Arithmetic Progression (AP)
The formula for the nth Arithmetic Progression is:
[tex]\begin{gathered} T_n=\text{ a + (n-1)d} \\ \text{Where T}_n=\text{ nth term} \\ a\text{ = first term} \\ n\text{ = number of terms} \\ d\text{ = common difference} \end{gathered}[/tex]The common difference, d = 30 - 60 = -30
The first term, a = 60
Substituting these parameters into the formula:
[tex]\begin{gathered} T_n=\text{ 60 + (n - 1)(-30)} \\ T_n=\text{ 60 + (-30n + 30)} \\ T_n=\text{ 60 -30n + 30} \\ T_n=\text{ 90 - 30n} \end{gathered}[/tex]