Sequence A uses 'add 4' starting from 0: (0, 4, 8, 12, 16). Sequence B uses 'add 8' starting from 0: (0, 8, 16, 24, 32). What is the relationship between corresponding terms?
AEach term in Sequence B is 4 more than the corresponding term in Sequence A
BEach term in Sequence B is twice the corresponding term in Sequence A
CThere is no consistent relationship — it changes at different term positions
DEach term in Sequence A is twice the corresponding term in Sequence B
At every position: 8 = 2×4, 16 = 2×8, 24 = 2×12, 32 = 2×16. The multiplicative relationship is constant because Sequence B's rule (add 8) is exactly double Sequence A's rule (add 4). The relationship between the rules determines the relationship between corresponding outputs. Option A is the common confusion — adding 4 describes the pattern *within* Sequence A, not the relationship *between* sequences.
Question 2 Multiple Choice
You pair corresponding terms from two sequences — 'add 3' and 'add 6,' both starting at 0 — as ordered pairs: (0,0), (3,6), (6,12), (9,18). When you plot these on a coordinate plane, what do you see?
AA curved arc that bends upward
BA zigzag pattern alternating high and low
CA straight line
DA random scatter with no visible pattern
When two sequences have a constant ratio between corresponding terms (here, 2:1), the ordered pairs fall on a straight line through the origin. A straight line through (0,0) is the geometric signature of a constant multiplicative relationship. This is the earliest encounter with what will later be called a linear function.
Question 3 True / False
The relationship between two paired sequences changes depending on which term position you examine — it is not constant.
TTrue
FFalse
Answer: False
When both sequences start at 0 and have constant rules, the ratio between corresponding terms is fixed at every position. If the first rule is 'add 3' and the second is 'add 6,' the second term is always exactly double the first — at position 1 (3 vs. 6), position 2 (6 vs. 12), position 10 (30 vs. 60), and so on. The consistency comes from the constant ratio between the two rules.
Question 4 True / False
If Sequence A uses 'add 5' and Sequence B uses 'add 10,' each term in Sequence B will always be exactly double the corresponding term in Sequence A.
TTrue
FFalse
Answer: True
Since 10 = 2 × 5, Sequence B adds twice as much per step as Sequence A. Starting both from 0: Sequence A is 0, 5, 10, 15, 20... and Sequence B is 0, 10, 20, 30, 40... Each term in B is exactly double the corresponding term in A. The multiplicative relationship between the rules is preserved in every pair of corresponding terms.
Question 5 Short Answer
Explain why the relationship between two paired sequences depends on the rules that generated them, not just on a few specific terms.
Think about your answer, then reveal below.
Model answer: Each sequence grows by adding a fixed amount per step. If one rule adds twice as much as the other, the outputs will always be in a 2:1 ratio — not by coincidence at one step, but consistently at every step. The relationship is built into the rules, so it holds for all corresponding pairs, and is why plotting the pairs produces a straight line.
Students who check only one or two pairs might think the relationship could be different elsewhere. But because both rules operate at a constant rate from the same starting point, the ratio between corresponding terms equals the ratio between the rules — permanently. This is what makes the relationship predictable enough to graph as a line.