Given the recursively defined formula a1=−3

Question

𝑎
1
=
−
3
, an=an−1+4
𝑎
𝑛
=
𝑎
𝑛
−
1
+
4
, determine which option is the correct function notation.(1 point)
Responses

a(1)=−3
𝑎
(
1
)
=
−
3
; f(n)=f(n−1)+4
𝑓
(
𝑛
)
=
𝑓
(
𝑛
−
1
)
+
4
a 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
(
1
)
=
−
3
; f(n)=f(an−1)+4
𝑓
(
𝑛
)
=
𝑓
(
𝑎
𝑛
−
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

f(1)=−3
𝑓
(
1
)
=
−
3
; f(n)=f(n−1)+4
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
(
1
)

Answer 1

The correct function notation that corresponds to the recursively defined formula \( a_1 = -3 \) and \( a_n = a_{n-1} + 4 \) is:

f(1) = -3; f(n) = f(n-1) + 4

This captures the initial condition and the recursive relationship accurately. Thus, the answer is:

f(1)=−3; f(n)=f(n−1)+4