### Solution
Let's work through each part of the question step by step.
#### Part (a) Completing the Table
We need to fill in the total number of dots for Step 1, Step 4, and Step 5.
From the given pattern:
- Step 2 has 9 dots.
- Step 3 has 17 dots.
Step 1:
To find the number of dots in Step 1, we observe the change in the number of dots from Step 2 to Step 3. There is an increase of [tex]\(17 - 9 = 8\)[/tex] dots.
Thus, to find the number of dots in Step 1, we subtract these 8 dots from the number of dots in Step 2.
[tex]\[ \text{Number of dots in Step 1} = 9 - 8 = 1 \][/tex]
Step 4:
The pattern continues with an increase of 8 dots per step. Therefore, to find the number of dots in Step 4:
[tex]\[ \text{Number of dots in Step 4} = 17 + 8 = 25 \][/tex]
Step 5:
Similarly, the number of dots in Step 5 will be:
[tex]\[ \text{Number of dots in Step 5} = 25 + 8 = 33 \][/tex]
Now we can complete the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Step & Total Number of Dots per Step \\
\hline
1 & 1 \\
\hline
2 & 9 \\
\hline
3 & 17 \\
\hline
4 & 25 \\
\hline
5 & 33 \\
\hline
\end{tabular}
\][/tex]
#### Part (b) Relationship and Differences with Question 1
While the details of Question 1 aren't provided, typically in pattern recognition problems involving dots, we try to identify the sequence and growth of the pattern.
Relationship:
The dots in this question show an arithmetic sequence wherein each step increases by a constant number, specifically 8 dots.
If Question 1 also involved a pattern of dots, it is possible that it might have also involved an arithmetic sequence or some pattern growth, showing a similar understanding of how patterns can be identified and extended.
Differences:
This specific pattern has a defined step differential of 8 dots. If Question 1 had a different increment or a non-arithmetic pattern (such as geometric or quadratic), then the method and rate of increase would be different. Differences might also include arrangement (e.g., linear vs. triangular) or how the sequence was derived.
In summary, while the principles of identifying the pattern remain constant, the specific increments and steps may differ from one question to another.
