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Find the Sequence Rule
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Find the Sequence Rule
Part 1: Find the Rule
For each sequence, find an equation for y in terms of x. Show the mathematical reasoning used to find your rule.
1. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 10, 17, 24, 31, 38
x: 1, 2, 3, 4, 5
y: 10, 17, 24, 31, 38
2. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 9, 15, 23, 33, 45
x: 1, 2, 3, 4, 5
y: 9, 15, 23, 33, 45
3. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 7, 12, 22, 42, 82
x: 1, 2, 3, 4, 5
y: 7, 12, 22, 42, 82
4. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 47, 38, 23, 2, −25
x: 1, 2, 3, 4, 5
y: 47, 38, 23, 2, −25
Part 2: Apply Your Reasoning
Find the rule for each sequence. Check your equation by substituting at least two values of x.
5. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 5, 10, 19, 32, 49
x: 1, 2, 3, 4, 5
y: 5, 10, 19, 32, 49
6. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 98, 96, 92, 84, 68
x: 1, 2, 3, 4, 5
y: 98, 96, 92, 84, 68
7. The sequence of values is shown below:
x: 1, 2, 3, 4, 5
y: 3.5, 5, 6.5, 8, 9.5
x: 1, 2, 3, 4, 5
y: 3.5, 5, 6.5, 8, 9.5
8. Explain how you can tell whether a sequence follows a linear rule or a non-linear rule.
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