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

NameDate

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

Jun's reading log: 7, 11, 15, 19, … What is the formula for term n? Simplify it.
Kira's bike-ride km log: 2, 11, 20, 29, … What is the formula for term n? Simplify it.
Milo tracks mL of juice left, in tens: 25, 21, 17, 13, … What is the formula for term n? Simplify it.
4.
Noah's sunflower-seed chart: 5, 15, 45, 135, … Which formula gives term n?
- a(n) = 5 + 10(n − 1)
- a(n) = 5 · 3^(n − 1)
- a(n) = 3 · 5^(n − 1)
- a(n) = 5 · 3^n
Tala paints ladder rungs with numbers: 3, 11, 19, 27, … What is term 40?
Bo draws branches on a tree picture: 6, 18, 54, 162, … What is term 7?
Esme builds a tile pattern. Stage 1 has 5 tiles, and each stage adds 3 tiles. How many tiles does stage 40 have?
Luz keeps cutting paper in half and stacking the halves. After step 1 the stack is 0.2 mm thick; each step doubles it (× 2). How many mm thick is it after step 8?
9.
Milo's list has the formula a(n) = 9 + 4(n − 1). Which recursive rule makes the same list?
- a(1) = 13, a(n) = a(n − 1) + 4
- a(1) = 9, a(n) = a(n − 1) + 4
- a(1) = 4, a(n) = a(n − 1) + 9
10.
Noah's list has the formula a(n) = 6n + 2. Which recursive rule makes the same list?
- a(1) = 6, a(n) = a(n − 1) + 2
- a(1) = 8, a(n) = a(n − 1) + 6
- a(1) = 2, a(n) = a(n − 1) + 6

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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