Introduction to Sequences Quick Check

Question

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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)=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(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

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)=f(an−1)+4

Answer 1

To determine the correct function notation based on the given recursively defined formula, let's analyze the information:

You have:

• The first term defined as \( a_1 = -3 \)
• The recursive formula given as \( a_n = a_{n-1} + 4 \)

We can express the sequence using function notation.

1. For the first term:

   • \( a(1) = -3 \) means that when \( n = 1 \), the value of the sequence is -3.

2. The recursive rule states that each term is the previous term plus 4. This can also be written in function notation as:

   • \( a(n) = a(n-1) + 4 \)

This matches the second option in your responses, which states:

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

So, the correct answer is:

f(1) = −3; f(n) = f(n−1) + 4.