Grade 9 · Math · Algebra 1

9th grade Formulas for the nth term of arithmetic and geometric sequences worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Formulas for the nth term of arithmetic and geometric sequences

Grade 9 Math Worksheet - Building Confidence

NameDate

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

Jun's pencil-count pattern has a formula. The formula is a(n) = 7 + 4(n − 1). What is a(20)?
Kira's block tower pattern has a formula. The formula is a(n) = 12 + 5(n − 1). What is a(30)?
Luz's countdown timer pattern has a formula. The formula is a(n) = 50 − 3(n − 1). What is a(11)?
Milo's paper-cutting pattern has a formula. The formula is a(n) = 3 · 2^(n − 1). What is a(6)?
1 | 9; 2 | 15; 3 | 21; … Every arrow: + 6. Ren sets out chairs in a growing pattern. Term 1 is 9 and every arrow is + 6. Term 25 is 24 arrows after term 1. What is term 25?
1 | 15; 2 | 19; 3 | 23; … Every arrow: + 4. Tala lines up crayons in a growing pattern. Term 1 is 15 and every arrow is + 4. Term 40 is 39 arrows after term 1. What is term 40?
1 | 100; 2 | 93; 3 | 86; … Every arrow: − 7. Zee's water tank drains in steady steps. Term 1 is 100 and every arrow is − 7. Term 13 is 12 arrows after term 1. What is term 13?
1 | 5; 2 | 10; 3 | 20; … Every arrow: × 2. Ari's cookie-sharing chart doubles each row. Term 1 is 5 and every arrow is × 2. Term 7 is 6 arrows after term 1. What is term 7?
1 | 3; 2 | 12; 3 | 48; … Every arrow: × 4. Bo's kite-club poster pattern grows. Term 1 is 3 and every arrow is × 4. Term 5 is 4 arrows after term 1. What is term 5?
1 | 7; 2 | 21; 3 | 63; … Every arrow: × 3. Esme's leaf-pattern drawing grows. Term 1 is 7 and every arrow is × 3. Term 5 is 4 arrows after term 1. What is term 5?

Formulas for the nth term. Every version has 10 questions, and the answer key prints on the second page.

I can find any term with a(n) = a(1) + d(n − 1) or a(n) = a(1) · r^(n − 1).
I can write the formula for term n from a list, and turn it into a recursive rule.
I can find which term has a given value, and a(1) from two terms.

Standard: F-BF.A.2, F-BF.A.1a, F-IF.A.3, F-LE.A.2

explicit formula: A rule that gives term n straight from n, with no earlier terms.

a(n): Term number n of the list.

common difference d: The number every arrow adds.

common ratio r: The number every arrow multiplies by.

n − 1: The number of arrows from term 1 to term n.

Your child counted n steps to term n instead of n − 1.

Your child combined the first term with the step before multiplying.

Your child multiplied by the power's number instead of using it as a power.

Ask: how many steps are there from term 1 to term 1?

Ask: in the formula, which part is multiplied first?

Ask: what does 2^5 mean, written out?

What is the most common mistake with formulas for the nth term of arithmetic and geometric sequences?

Your child counted n steps to term n instead of n − 1.

How can I help my child with formulas for the nth term of arithmetic and geometric sequences?

Ask: how many steps are there from term 1 to term 1?

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.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records