To identify the relationship between the corresponding terms of the two given patterns, we can analyze their terms step-by-step.
Let's start by listing out the terms of each pattern according to their given rules:
### Pattern A:
The rule for Pattern A is to start at 0 and add 2 for each subsequent term. Therefore, the terms of Pattern A are:
[tex]\[ 0, 2, 4, 6, 8 \][/tex]
### Pattern B:
The rule for Pattern B is to start at 0 and add 4 for each subsequent term. Therefore, the terms of Pattern B are:
[tex]\[ 0, 4, 8, 12, 16 \][/tex]
Now, let's pair the corresponding terms from both patterns:
1. (0, 0)
2. (2, 4)
3. (4, 8)
4. (6, 12)
5. (8, 16)
Next, we need to examine the relationship between each pair of corresponding terms. Specifically, we will see how each term in Pattern B relates to the corresponding term in Pattern A. Analyzing them one by one:
- For the pair (0, 0): Since both are zero, we cannot define a ratio here. Thus, we denote it as undefined or None.
- For the pair (2, 4): The second term (4) is two times the first term (2). The relationship here is a multiplication by 2.
- For the pair (4, 8): The second term (8) is two times the first term (4). Again, the relationship is a multiplication by 2.
- For the pair (6, 12): The second term (12) is two times the first term (6). The relationship here is also a multiplication by 2.
- For the pair (8, 16): The second term (16) is two times the first term (8). The relationship is multiplication by 2.
From this analysis, we can conclude that:
- For terms where the term in Pattern A is not zero (2, 4, 6, 8), the term in Pattern B is always twice the corresponding term in Pattern A.
- This relationship is consistent for most pairs, except the initial pair where both terms are zero.
Therefore, the relationship between the corresponding terms of these two patterns (excluding the initial term) is that each term in Pattern B is twice the corresponding term in Pattern A. When considering all terms, be aware that the first pair does not define a relationship due to both values being zero.
