Grade 9 · Math · Algebra 1

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

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Formulas for the nth term of arithmetic and geometric sequences

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Tala's practice log: 12, 16, 20, … Which term number is 140?
Ari's toy-train track pieces: 18, 24, 30, … Which term number is 330?
Bo's robot doubles its score each level: 3, 6, 12, … Which term number is 768?
Esme's star-pattern stages: 4, 12, 36, … Which term number is 972?
Jun's hiking map marks an arithmetic sequence with a(3) = 10 and a(9) = 52. What is a(1)?
Luz's box-stacking chart shows an arithmetic sequence with a(4) = 50 and a(6) = 80. What is a(1)?
Milo's kite-string log shows an arithmetic sequence with a(2) = 17 and a(6) = 57. What is a(1)?
8.
Noah's plant is 10 cm tall at week 0 and grows 3 cm each week. Which formula gives its height h after n weeks?
- h = 10 + 3n
- h = 3 + 10n
- h = 10 + 3(n − 1)
9.
A science video shows Pia a dish with 200 bacteria at hour 0. The number doubles every hour. Which formula gives the bacteria b after n hours?
- b = 200 · 2^n
- b = 200 + 2n
- b = 200 · 2^(n − 1)
10.
Tala's game power bar is 120 points at round 0 and keeps 1/2 of its points each round. Which formula gives the points p after n rounds?
- p = 120 · (1/2)^n
- p = 120 + (1/2)n
- p = 120 · (1/2)^(n − 1)

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.

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