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

NameDate

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

1.
Ari's phone-tree chart for a club picnic shows the list 4, 12, 36, 108. Is the list arithmetic, geometric or neither?
- Geometric: × 3 on every arrow
- Arithmetic: + 8 on every arrow
- Neither: the arrows change
2.
Esme's bake-sale tally shows the list 2, 6, 18, 30. Is the list arithmetic, geometric or neither?
- Arithmetic: + 4 on every arrow
- Geometric: × 3 on every arrow
- Neither: the arrows change
3.
Jun's math-club handout shows the list 81, 27, 9, 3. Is the list arithmetic, geometric or neither?
- Arithmetic: − 54 on every arrow
- Geometric: × 1/3 on every arrow
- Neither: the arrows change
Luz's class uses a phone tree for a trip. The people told in rounds 1 to 4 are 5, 10, 20, 40. What is the next term?
Noah's robot token jumps the same amount each turn on a number line. Its spots are 14, 9, 4, -1. What is the next term?
Pia's quiz-game score changes by the same amount each round. The scores are 10, 4, -2, -8. What is the next term?
Zee's phone game scores grow. The rule is a(1) = 2, a(n) = 5 · a(n − 1). What is a(4)?
Bo reads 12 pages on day 1 of a reading challenge, then 5 more pages each day than the day before. How many pages does Bo read on day 6?
A science video shows 300 bacteria in a dish at count 1. The number doubles (× 2) at each count, 20 minutes apart. How many bacteria does Kira see at count 5?
Luz drops a play ball from shoulder height. Bounce 1 reaches 80 cm, and each bounce is 1/2 as high as the one before. How high, in cm, is bounce 4?

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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