The values in the table represent a linear function. What is the common difference of the associated arithmetic sequence?

[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 7 \\
\hline
2 & 26 \\
\hline
3 & 45 \\
\hline
4 & 64 \\
\hline
5 & 83 \\
\hline
\end{array}
\][/tex]

A. 24
B. 1
C. 19
D. 38



Answer :

To determine the common difference of the associated arithmetic sequence for the given values in the table:

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
1 & 7 \\
\hline
2 & 26 \\
\hline
3 & 45 \\
\hline
4 & 64 \\
\hline
5 & 83 \\
\hline
\end{tabular}

We need to calculate the difference between consecutive [tex]$y$[/tex] values. The steps are as follows:

1. Calculate [tex]\( y_2 - y_1 \)[/tex]:
[tex]\[ 26 - 7 = 19 \][/tex]

2. Calculate [tex]\( y_3 - y_2 \)[/tex]:
[tex]\[ 45 - 26 = 19 \][/tex]

3. Calculate [tex]\( y_4 - y_3 \)[/tex]:
[tex]\[ 64 - 45 = 19 \][/tex]

4. Calculate [tex]\( y_5 - y_4 \)[/tex]:
[tex]\[ 83 - 64 = 19 \][/tex]

We see that the difference between each pair of consecutive [tex]$y$[/tex] values is the same (19). Therefore, the common difference of the arithmetic sequence is 19.

Thus, the correct answer is:
C. 19