What is the rule for this pattern: 100, 90, 80, 70, 60?
AMultiply by 10 each time
BSubtract 10 each time
CDivide by 10 each time
DAdd 10 each time
Each term is 10 less than the one before it: 100 - 10 = 90, 90 - 10 = 80, and so on. The rule is 'subtract 10 each time.' This is a decreasing pattern — not all patterns go up. The constant difference (10) between consecutive terms is the signature of an additive (or in this case, subtractive) pattern.
Question 2 Multiple Choice
Two patterns both have 4 as their second term: Pattern A is 2, 4, 6, 8, 10 and Pattern B is 2, 4, 8, 16, 32. Why do they produce completely different sequences despite starting the same way?
AThey use different starting numbers
BPattern A adds 2 each time while Pattern B multiplies by 2 each time — different rules produce different sequences even from the same start
CPattern B has an error after the 4
DBoth patterns actually produce the same sequence
Pattern A follows the rule 'add 2' (differences are constant: 2, 2, 2, 2). Pattern B follows the rule 'multiply by 2' (each term is double the previous one). They share the first two terms (2, 4) by coincidence, but the rules are fundamentally different. This is why identifying the rule — not just the next term — matters: the same starting terms can lead to wildly different patterns.
Question 3 True / False
Nearly every number pattern should increase — the numbers should get bigger each time.
TTrue
FFalse
Answer: False
Patterns can decrease (subtract each time: 50, 45, 40, 35), stay constant (5, 5, 5, 5), or alternate (1, 3, 1, 3). The defining feature of a pattern is a predictable rule, not the direction of change. Decreasing patterns are just as valid and important as increasing ones.
Question 4 Short Answer
Explain why the rule of a number pattern is more useful than just knowing the next term.
Think about your answer, then reveal below.
Model answer: The rule lets you find any term in the pattern without listing them all. If you only know the next term, you can extend one step. But if you know the rule (for example, 'add 7 each time, starting at 3'), you can find the 100th term, check whether a specific number belongs to the pattern, and explain why the pattern works. The rule is the complete description; a single next term is just one data point.
This is the transition from arithmetic to algebraic thinking. Knowing the rule 'add 7, start at 3' is equivalent to the formula 3 + 7n (which students will encounter later). The rule generalizes — it answers every possible question about the pattern, not just 'what comes next?'