Given the rule "Add 3", and the starting number 3, and given the rule "Add 9", and the starting number 9, identify the relationship between corresponding terms:

Let's break this down based on the two rules:

1. **First Sequence**: Starting number is 3, and the rule is "Add 3".
   - The terms of this sequence would be:  
   3, 6, 9, 12, 15, 18, 21, 24, ...

   Each term is obtained by adding 3 to the previous term.

2. **Second Sequence**: Starting number is 9, and the rule is "Add 9".
   - The terms of this sequence would be:  
   9, 18, 27, 36, 45, 54, 63, 72, ...

   Each term is obtained by adding 9 to the previous term.

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### Corresponding Terms:
The corresponding terms are:
- First terms: 3 (from first sequence), 9 (from second sequence)
- Second terms: 6 (from first sequence), 18 (from second sequence)
- Third terms: 9 (from first sequence), 27 (from second sequence)
- Fourth terms: 12 (from first sequence), 36 (from second sequence)
- ...

### Relationship:
For each pair of corresponding terms, the term in the second sequence is always **3 times** the term in the first sequence.

- \( 9 = 3 \times 3 \)
- \( 18 = 3 \times 6 \)
- \( 27 = 3 \times 9 \)
- \( 36 = 3 \times 12 \)

So, the relationship between corresponding terms is that each term in the second sequence is **3 times** the value of the corresponding term in the first sequence.

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Would you like more details on this or have any further questions?

Here are 5 questions that build on this:
1. What would the relationship be if the second sequence added 6 instead of 9?
2. How would the relationship change if the first sequence started at 5 and added 5?
3. What if both sequences started at 0 but followed the same rules (Add 3 and Add 9)?
4. Can you find the general formula for the nth term in both sequences?
5. What would happen if instead of addition, we used multiplication rules?

**Tip**: Identifying a pattern between sequences often involves observing how the terms change relative to each other (like multiplication or addition differences).

Given the rule 'Add 3', and the starting number 3, and given the rule 'Add 9', and the starting number 9, identify the relationship between corresponding terms.

Explore the relationship between two arithmetic sequences where one starts at 3 and adds 3, while the other starts at 9 and adds 9. Learn how each term in the second sequence is 3 times the corresponding term in the first sequence. Ideal for students in Grades 5-7.

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