Given the recursively defined formula a1=−3

Question

, 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)=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
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(n)=an−1+4

Answer 1

To express the recursively defined sequence using function notation correctly based on the given information, we analyze the definitions first:

1. The initial condition is given as \( a_1 = -3 \).
2. The recursive definition states \( a_n = a_{n-1} + 4 \).

The closest match from the options involves function notation using \( f \), where:

• \( f(1) = -3 \): This corresponds to the initial value \( a_1 = -3 \).
• \( f(n) = f(n-1) + 4 \): This corresponds to the recursive relationship \( a_n = a_{n-1} + 4 \).

Thus, the correct representation in function notation would be:

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

So the correct response is:

f(1)=−3; f(n)=f(n−1)+4