To compare Katie's and Gina's patterns, let's examine how each sequence is generated.
Katie's pattern:
- 0, 8, 16, 24, 32, ...
- This can be expressed as \( 8n \) where \( n \) is the term index (0, 1, 2, ...).
- For example:
- \( n = 0: 8 \times 0 = 0 \)
- \( n = 1: 8 \times 1 = 8 \)
- \( n = 2: 8 \times 2 = 16 \)
- \( n = 3: 8 \times 3 = 24 \)
- \( n = 4: 8 \times 4 = 32 \)
Gina's pattern:
- 0, 16, 32, 48, 64, ...
- This can be expressed as \( 16n \) where \( n \) is the term index (0, 1, 2, ...).
- For example:
- \( n = 0: 16 \times 0 = 0 \)
- \( n = 1: 16 \times 1 = 16 \)
- \( n = 2: 16 \times 2 = 32 \)
- \( n = 3: 16 \times 3 = 48 \)
- \( n = 4: 16 \times 4 = 64 \)
Now, to find the relationship, we can compare corresponding terms:
-
For \( n = 0 \):
- Katie: \( 0 \)
- Gina: \( 0 \)
-
For \( n = 1 \):
- Katie: \( 8 \)
- Gina: \( 16 \)
- Relationship: \( 16 = 2 \times 8 \)
-
For \( n = 2 \):
- Katie: \( 16 \)
- Gina: \( 32 \)
- Relationship: \( 32 = 2 \times 16 \)
-
For \( n = 3 \):
- Katie: \( 24 \)
- Gina: \( 48 \)
- Relationship: \( 48 = 2 \times 24 \)
-
For \( n = 4 \):
- Katie: \( 32 \)
- Gina: \( 64 \)
- Relationship: \( 64 = 2 \times 32 \)
From all the calculations, we can conclude that each term in Gina's pattern is indeed 2 times as much as the corresponding term in Katie's pattern.
Thus, the correct answer is:
A. Each term in Gina's pattern is 2 times as much as the corresponding term in Katie's pattern.
1 answer