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Pattern Rules and Equations
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Pattern Rules and Equations
A space probe is sending number patterns back to mission control. For each sequence, look for the change between terms, then connect the term number to the value. Use n for the term number. Show enough working to explain your rule.
Decode the signals
Each signal follows a pattern rule. Use the term number n to describe the value.
1.Signal A reads 4, 7, 10, 13, ... What is the constant change, the next two terms, and an equation for the value of term n?
2.Signal B counts down: 18, 13, 8, 3, ... Write the constant change and an equation for term n. What is the 6th term?
3.Isla records probe power levels: 6, 12, 18, 24, ... Which equation gives the value of term n?
- 6n
- n + 6
- 6n + 1
- 12n
4.Mere spots a faulty signal: 2, 5, 9, 14, 20, ... Is its change constant? Explain by finding the changes between consecutive terms.
Equations at mission control
Use substitution and inverse operations to check the probe's calculations.
5.Zoe's sequence rule is 4n + 2. Find the first four terms by substituting n = 1, 2, 3 and 4.
6.A probe sends 29 data packets. The rule is 5n + 4, where n is the number of the transmission stage. Which stage sent 29 packets?
7.Solve the mission equation 3x + 7 = 25. Show the inverse operations you use.
8.A sequence has the rule 7n - 2. True or false: its 4th term is 26. Check by substituting n = 4.
TrueFalse
9.Create a linear pattern with a constant change of +4. Write its first five terms and a rule using n. Choose a starting term that is not zero.
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