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 - Building Confidence

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

Every arrow between rows: + 6. Ari's bean plant grows the same amount each week. The growth table shows its height in cm. What is term 6?
Every arrow between rows: × 2. Bo folds a sheet of paper in half, again and again. The growth table shows how many layers there are after each fold. What is term 6?
Every arrow between rows: − 4. Esme hands out star stickers each round. The growth table shows how many are left after each round. What is term 6?
Every arrow between rows: × 3. Jun builds a block pattern that grows by the same factor. The growth table shows the blocks in each stage. What is term 6?
Read this first
Growth table
term number n term
1 450
2 380
3 310
4 240
Kira drinks the same amount of water between stops on a hike. The growth table shows the mL left at each stop. Every arrow adds the same number. What number goes on each arrow?
Noah draws a star pattern for art club. The growth table shows the stars in each stage. Every arrow multiplies by the same number. What number goes on each arrow?
Pia's pencil-case pattern uses the rule a(n) = a(n − 1) + 7, with a(1) = 4. So a(2) = 4 + 7 = 11. What is a(4)?
Ren's robot's number game uses the rule a(n) = 2 · a(n − 1), with a(1) = 5. So a(2) = 2 · 5 = 10. What is a(5)?
Tala's countdown game uses the rule a(n) = a(n − 1) − 3, with a(1) = 40. So a(2) = 40 − 3 = 37. What is a(6)?
Zee's drum-beat pattern uses the rule a(n) = 4 · a(n − 1), with a(1) = 3. So a(2) = 4 · 3 = 12. What is a(4)?

term number n	term
1	450
2	380
3	310
4	240

9th grade Arithmetic, geometric or neither? Find the next terms with a recursive rule worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

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

What your child will learn

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

Words to know

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.

Common mistakes

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.

What to say

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?

Questions parents ask

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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