Respuesta :
Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula [tex]f(n+1)=f(n)+2.5[/tex]
Explanation:
The given recursive formula is [tex]f(n+1)=f(n)+2.5[/tex] for [tex]n\geq 1[/tex] and [tex]f(1)=-10[/tex]
We need to determine the sequence.
The sequence can be determined by substituting n = 1, 2, 3, 4,....
2nd term of the sequence:
Substituting n = 1 in the formula [tex]f(n+1)=f(n)+2.5[/tex], we get,
[tex]f(1+1)=f(1)+2.5[/tex]
Simplifying, we have,
[tex]f(2)=-10+2.5=-7.5[/tex]
Thus, the 2nd term of the sequence is -7.5
3rd term of the sequence:
Substituting n = 2 in the formula [tex]f(n+1)=f(n)+2.5[/tex], we get,
[tex]f(2+1)=f(2)+2.5[/tex]
Simplifying, we have,
[tex]f(3)=-7.5+2.5=-5[/tex]
Thus, the 3rd term of the sequence is -5
4th term of the sequence:
Substituting n = 3 in the formula [tex]f(n+1)=f(n)+2.5[/tex], we get,
[tex]f(3+1)=f(3)+2.5[/tex]
Simplifying, we have,
[tex]f(4)=-5+2.5=-2.5[/tex]
Thus, the 4th term of the sequence is -2.5
Therefore, the sequence is –10, –7.5, –5, –2.5, …
Hence, Option C is the correct answer.
