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Find the Sequence Rule

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Find the Sequence Rule

For each sequence, find a rule for y in terms of x. Use differences or another pattern to justify your rule, then check it against the given terms.

Investigate the patterns

1.Sequence A models a linear relationship. Find the rule for y in terms of x, and show how the constant difference helps you find it.

2.For Sequence B, calculate the first and second differences. Use them to find a quadratic rule for y in terms of x.

3.A sequence starts 7, 12, 22, 42, 82 for x = 1, 2, 3, 4, 5. Each term is formed by doubling the previous term and subtracting 2. Write an exponential rule for y in terms of x.

4.For x = 1, 2, 3, 4, 5, a sequence has y-values 47, 38, 23, 2, −25. The rule is quadratic. Find its rule and state the constant second difference.

Apply and explain

5.A pattern has y-values 5, 10, 19, 32, 49 when x = 1, 2, 3, 4, 5. Find a quadratic rule and verify it for x = 2 and x = 5.

6.A sequence has y-values 98, 96, 92, 84, 68 for x = 1, 2, 3, 4, 5. Notice how the amounts subtracted double each time. Find a rule for y in terms of x.

7.A linear sequence begins 3.5, 5, 6.5, 8, 9.5 for x = 1, 2, 3, 4, 5. Find the rule, then predict the value when x = 12.

8.A classmate says, “If the first differences are not constant, there can’t be a useful rule.” Explain why this is incorrect. Include one way to recognise a quadratic pattern.