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A sequence formula is a mathematical rule that defines the pattern of a sequence by expressing each term as a function of its position, denoted by \( n \). In this exercise, the sequence formula is \( a_n = \frac{n}{2} + 1 \), where \( n \) is a non-negative integer \( n \geq 0 \). This formula allows us to generate each term in the sequence.
To understand this formula, note how each term can be obtained by plugging in different values for \( n \):

• When \( n = 0 \), the term is \( 1 \).
• When \( n = 1 \), the term is \( 1.5 \).
• For \( n = 2 \), the term is \( 2 \).
• If \( n = 3 \), the term becomes \( 2.5 \).
• And for \( n = 4 \), the term is \( 3 \).

By using the sequence formula, you can easily calculate any term in the sequence.

Plotting points involves placing visual markers where a term's value meets its corresponding position on a graph. Each term from the sequence represents a point on the graph, with the x-coordinate corresponding to \( n \) and the y-coordinate to \( a_n \).
For the sequence \( a_n = \frac{n}{2} + 1 \), the points you'd plot are:

• \( (0, 1) \)
• \( (1, 1.5) \)
• \( (2, 2) \)
• \( (3, 2.5) \)
• \( (4, 3) \)

Each point represents the term value of the sequence at a specific position. These points help visualize how the sequence behaves as \( n \) increases. When plotted on a coordinate plane, they show a clear trend, helping make the relationship between \( n \) and \( a_n \) more understandable.

To calculate the terms of the sequence using the formula \( a_n = \frac{n}{2} + 1 \), substitute different values of \( n \) into the formula. This is a straightforward process because you simply replace \( n \) with the position number to find the term. Let's look at the first few terms:

• For \( n = 0 \), substituting into the formula gives \( a_0 = \frac{0}{2} + 1 = 1 \).
• When \( n = 1 \), it produces \( a_1 = \frac{1}{2} + 1 = 1.5 \).
• If we put \( n = 2 \), we get \( a_2 = \frac{2}{2} + 1 = 2 \).
• Substituting \( n = 3 \) yields \( a_3 = \frac{3}{2} + 1 = 2.5 \).
• Finally, for \( n = 4 \), we find \( a_4 = \frac{4}{2} + 1 = 3 \).

These calculations demonstrate the step-by-step process of determining each term using the formula, providing the understanding needed to compute any further terms in the sequence.

The coordinate plane is a two-dimensional space where each point is defined by a pair of numbers - the x-coordinate and the y-coordinate. These are its horizontal and vertical positions, respectively.
In the context of sequences, the coordinate plane is used to plot the graphical representation of the sequence. The x-axis typically represents the position number \( n \) of the term, while the y-axis reflects the term value \( a_n \). By plotting the sequence terms as points on this plane, you can visually analyze the sequence's progression.
In our exercise with the sequence formula \( a_n = \frac{n}{2} + 1 \), when you plot the first five terms:

• \( (0, 1) \)
• \( (1, 1.5) \)
• \( (2, 2) \)
• \( (3, 2.5) \)
• \( (4, 3) \)

You can see a linear pattern on the graph. This trend emphasizes the consistent nature of this linear sequence, making the relationship more intuitive to grasp.