To determine the common difference of the associated arithmetic sequence from the given table, we need to follow these steps:
1. Identify the [tex]\( y \)[/tex]-values from the table:
[tex]\[
y(1) = 9, \quad y(2) = 22, \quad y(3) = 35, \quad y(4) = 48, \quad y(5) = 61
\][/tex]
2. Calculate the differences between each successive pair of [tex]\( y \)[/tex]-values:
[tex]\[
y(2) - y(1) = 22 - 9 = 13
\][/tex]
[tex]\[
y(3) - y(2) = 35 - 22 = 13
\][/tex]
[tex]\[
y(4) - y(3) = 48 - 35 = 13
\][/tex]
[tex]\[
y(5) - y(4) = 61 - 48 = 13
\][/tex]
3. Observe the calculated differences:
[tex]\[
\{ 13, 13, 13, 13 \}
\][/tex]
4. Since all the differences are the same, we can conclude that the common difference of the associated arithmetic sequence is 13.
Therefore, the common difference of the associated arithmetic sequence is [tex]\(\boxed{13}\)[/tex].
