Question

Here is the recursive definition of a sequence.

f(0) = 20
f(n)=f(n-1)-4 for n ≥ 1
Graph the value of the term f(n) as a function of the term n for the first four terms of the sequence.
Slide each point up or down into the correct place.
4
80
€10
2
6
12
8
20
18
16
14
●2

Answer 1

Step-by-step explanation: To graph the value of the term f(n) as a function of the term n for the first four terms of the sequence, let's start by applying the recursive definition to find the values of f(n).

Using the given recursive definition:

f(0) = 20

f(n) = f(n-1) - 4 for n ≥ 1

Let's calculate the values of f(n) for n = 0, 1, 2, and 3:

For n = 0:

f(0) = 20

For n = 1:

f(1) = f(1-1) - 4 = f(0) - 4 = 20 - 4 = 16

For n = 2:

f(2) = f(2-1) - 4 = f(1) - 4 = 16 - 4 = 12

For n = 3:

f(3) = f(3-1) - 4 = f(2) - 4 = 12 - 4 = 8

Now, let's plot these values on a graph, with the term n on the x-axis and the value of f(n) on the y-axis:

Point A: (0, 20)

Point B: (1, 16)

Point C: (2, 12)

Point D: (3, 8)

To graph these points, slide each point up or down into the correct place:

Point A: (0, 20) ●

Point B: (1, 16) ●

Point C: (2, 12) ●

Point D: (3, 8) ●

Now, connect these points with a line:

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●

●

●

This graph represents the values of the sequence f(n) for the first four terms, with the x-axis representing the term number (n) and the y-axis representing the value of f(n). The line connects the points (0, 20), (1, 16), (2, 12), and (3, 8).