Question

write the function of the graphed arithmetic sequence.
(1 point)
the function of the arithmetic sequence is \boxed{}.

Explanation:

Step1: Recall arithmetic sequence formula

An arithmetic sequence function has the form \( f(x)=a_1+(x - 1)d \), but when graphed as a linear function, it can also be written in slope - intercept form \( y=mx + b \), where \( m \) is the common difference (slope) and \( b \) is the initial term (\( a_1 \) when \( x = 0 \)).

Step2: Find the slope (common difference)

We can use two points, say \( (0,13) \) and \( (1,20) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{20 - 13}{1 - 0}=7 \).

Step3: Determine the y - intercept

From the point \( (0,13) \), we know that when \( x = 0 \), \( y = 13 \). So the y - intercept \( b = 13 \).

Step4: Write the function

Using the slope - intercept form \( y=mx + b \), with \( m = 7 \) and \( b = 13 \), the function is \( y = 7x+13 \).

Answer:

\( y = 7x + 13 \)