Question

Given the recursively defined formula a1=−3
, an=an−1+4
, determine which option is the correct function notation.(1 point)
Responses

f(1)=−3
; f(n)=f(n−1)+4
f left parenthesis 1 right parenthesis equals negative 3 ; f left parenthesis n right parenthesis equals f left parenthesis n minus 1 right parenthesis plus 4

f(1)=−3
; f(n)=an−1+4
f left parenthesis 1 right parenthesis equals negative 3 ; f left parenthesis n right parenthesis equals a subscript n minus 1 baseline plus 4

f(1)=−3
; f(n)=f(an−1)+4
f left parenthesis 1 right parenthesis equals negative 3 ; f left parenthesis n right parenthesis equals f left parenthesis a subscript n minus 1 baseline right parenthesis plus 4

a(1)=−3
; f(n)=f(n−1)+4

Answer 1

To express the recursively defined sequence using function notation, we need to align the definitions correctly.

The original definition is:
- \( a_1 = -3 \)
- \( a_n = a_{n-1} + 4 \)

In function notation, we can denote the sequence as \( f(n) \) where:
- \( f(1) = -3 \)
- \( f(n) = f(n - 1) + 4 \)

Thus, the correct option that reflects this definition is:

**f(1)=−3 ; f(n)=f(n−1)+4**

This notation accurately represents the defined recursive relationship.