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Linear Patterns Exploration

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Linear Patterns Exploration

For each pattern, look for the change between consecutive terms. Use n for the term number and T for the term value.

Spotting Linear Patterns

1.A sequence has term numbers 1, 2, 3, 4, 5 and values 6, 10, 14, 18, 22. What is the constant change in value each time?

2.A pattern starts at 31 and decreases by 5 each term. Write the values for terms 1 to 5.

3.Which sequence has a constant difference between consecutive terms?

3, 6, 12, 24, 48
7, 11, 15, 19, 23
2, 5, 10, 17, 26
4, 8, 9, 13, 18

4.A pattern has values 12, 17, 22, 27 for terms 1, 2, 3, 4. Is it linear? Give the constant difference to support your answer.

Rules and Tables

5.For the pattern with values 8, 13, 18, 23 at terms 1, 2, 3, 4, write a rule linking term number n to value T.

6.Use the rule T = 4n + 3 to find the values for term numbers 1, 2, 3, 5 and 8.

7.Match each rule to the description of its pattern. In each description, the starting value is the value at term 1.

T = 6n
T = 3n + 5
T = 11 - 2n
T = 5n - 4

Starts at 6 and increases by 6
Starts at 1 and increases by 5
Starts at 9 and decreases by 2
Starts at 8 and increases by 3

8.A sequence follows T = 7n - 2. Find the values at terms 1, 4 and 10.

Predictions and Graphing

9.A pattern follows T = 3n + 2. Find the value at term 12.

10.A rainwater tank contains 420 litres after 1 minute, 570 litres after 2 minutes, and 720 litres after 3 minutes. How many litres are added each minute?

11.A rainwater tank contains 420 litres after 1 minute, 570 litres after 2 minutes, and 720 litres after 3 minutes. Write a rule for the amount T in litres after n minutes.

12.A rainwater tank contains 420 litres after 1 minute, 570 litres after 2 minutes, and 720 litres after 3 minutes. Use the pattern to predict the amount after 6 minutes.

13.For the rule T = 2n + 4, complete the ordered pairs (n, T) for n = 1, 2, 3, 4 and 5.

14.How can you check from a table of term numbers and values whether a pattern is linear?