Grade 9 · Math · Algebra 1

9th grade Arithmetic, geometric or neither? Find the next terms with a recursive rule worksheet

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Arithmetic, geometric or neither? Find the next terms with a recursive rule

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Milo's practice minutes are arithmetic over 4 days: 8, ?, ?, 26. What is the second term?
Pia's crayon box count is arithmetic over 4 weeks: 50, ?, ?, 14. What is the second term?
Ren's flower count is geometric: 4, ?, 100. Every term is positive. What is the missing term?
4.
Zee's list is 4, 10, 16, 22. Which recursive rule makes this list?
- a(1) = 4, a(n) = a(n − 1) + 6
- a(1) = 6, a(n) = a(n − 1) + 4
- a(n) = a(n − 1) + 6, with no a(1)
5.
Bo's list is 40, 33, 26, 19. Which recursive rule makes this list?
- a(1) = 40, a(n) = a(n − 1) − 7
- a(1) = 40, a(n) = a(n − 1) + 7
- a(n) = a(n − 1) − 7, with no a(1)
6.
Esme's list is 5, 20, 80, 320. Which recursive rule makes this list?
- a(1) = 5, a(n) = 1/4 · a(n − 1)
- a(1) = 5, a(n) = 4 · a(n − 1)
- a(1) = 4, a(n) = 5 · a(n − 1)
7.
Jun's list is 64, 16, 4, 1. Which recursive rule makes this list?
- a(1) = 64, a(n) = 4 · a(n − 1)
- a(1) = 64, a(n) = a(n − 1) − 48
- a(1) = 64, a(n) = 1/4 · a(n − 1)
8.
Kira's list is 90, 75, 60, 45. Which recursive rule makes this list?
- a(1) = 15, a(n) = a(n − 1) − 90
- a(1) = 90, a(n) = a(n − 1) + 15
- a(1) = 90, a(n) = a(n − 1) − 15
Luz's rocket game doubles the score and then takes 1 away each round. The rule is a(1) = 3, a(n) = 2 · a(n − 1) − 1. What is a(4)?
Noah writes a number trick on paper at math club. The rule is a(1) = 1, a(n) = 2 · a(n − 1) + 4. What is a(5)?

Arithmetic, geometric or neither. Every version has 10 questions, and the answer key prints on the second page.

I can tell whether a list adds the same amount, multiplies by the same factor, or neither.
I can find the next terms, and any term, from a recursive rule.
I can pick the recursive rule, with its first term, that makes a list.

Standard: F-IF.A.3, F-BF.A.1a

sequence: A list of numbers in order: term 1, term 2, term 3 …

arithmetic sequence: Every arrow adds the same number (the common difference).

geometric sequence: Every arrow multiplies by the same number (the common ratio).

recursive rule: A start, a(1), and how to get each term from the one before.

a(n − 1): The term just before term n.

Your child used the rule the right way but stopped one step early.

Your child used the rule the right way but went one step too far.

Your child used the rule one time too many, counting from term 0 instead of term 1.

Ask: how many arrows are there from the row you know to the row you need?

Ask: how many arrows are there between the last row and the row you need?

Ask: how many arrows are there from term 1 to the term you need?

What is the most common mistake with arithmetic, geometric or neither? find the next terms with a recursive rule?

Your child used the rule the right way but stopped one step early.

How can I help my child with arithmetic, geometric or neither? find the next terms with a recursive rule?

Ask: how many arrows are there from the row you know to the row you need?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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