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
