Question

fill in the missing values of the arithmetic sequence in the table. then, use the table to write a function that represents the arithmetic sequence. (2 points) \\(\

$$\begin{array}{|c|c|}\\hline x & f(x) \\\\ \\hline 0 & \\square \\\\ \\hline 1 & 11 \\\\ \\hline 2 & 15 \\\\ \\hline 3 & \\square \\\\ \\hline \\end{array}$$

\\) the function for the arithmetic sequence is \\(f(x)=\square\\).

Explanation:

Step1: Find the common difference

In an arithmetic sequence, the common difference \( d \) is the difference between consecutive terms. Using \( x = 1 \) ( \( f(1)=11 \)) and \( x = 2 \) ( \( f(2)=15 \)):
\( d = f(2)-f(1)=15 - 11 = 4 \)

Step2: Find \( f(0) \)

For an arithmetic sequence, \( f(0)=f(1)-d \). Substitute \( f(1)=11 \) and \( d = 4 \):
\( f(0)=11 - 4 = 7 \)

Step3: Find \( f(3) \)

Using the common difference, \( f(3)=f(2)+d \). Substitute \( f(2)=15 \) and \( d = 4 \):
\( f(3)=15 + 4 = 19 \)

Step4: Write the function

The general form of an arithmetic sequence function is \( f(x)=f(0)+dx \). We know \( f(0)=7 \) and \( d = 4 \), so:
\( f(x)=7 + 4x \)

Answer:

• Missing value at \( x = 0 \): \( 7 \)
• Missing value at \( x = 3 \): \( 19 \)
• Function: \( f(x)=4x + 7 \)