Free Printable WorksheetMathAlgebra IIMath CurriculumALG2.182

ALG2.182 Sequences as Functions Worksheet

Download our free printable Algebra II Math worksheet on ALG2.182 Sequences as Functions. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.182 Sequences as Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.182 Sequences as Functions - Practice questions for Sequences as Functions.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.182 Sequences as Functions skill assessments:

Problem 1Difficulty: Mastery

Sequence p₀ = 2, p₁ = 5, and pₙ = 4pₙ₋₁ − 4pₙ₋₂ for n ≥ 2. Which explicit formula matches?

Apₙ = (n + 4)·2ⁿ

Bpₙ = (n + 2)·2ⁿ⁻¹

Cpₙ = (n + 4)·2ⁿ⁻¹

Dpₙ = 4·2ⁿ − 3

Solution & Explanation:The characteristic equation is r²−4r+4=0, a repeated root r=2, so pₙ=(c₁+c₂n)2ⁿ. Using p₀=2 and p₁=5 gives pₙ=(n+4)·2ⁿ⁻¹.

Problem 2Difficulty: Mastery

A sequence function A: ℤ → ℤ is defined by A(0)=0. For n ≥ 0: A(n+1)=A(n)+1. For n ≤ 0: A(n−1)=A(n)+1. Find A(−12).

Solution & Explanation:From A(0)=0, going to the left adds 1 each step: A(−1)=1, A(−2)=2, …, so A(−12)=12.

Problem 3Difficulty: Mastery

Explicit formula: wₙ = (n − 1)·3ⁿ⁻¹ for n = 1,2,3,… Which recursion is equivalent?

Aw₁ = 0; wₙ = wₙ₋₁ + 3ⁿ⁻¹

Bw₁ = 0; wₙ = 3wₙ₋₁ + 3ⁿ⁻²

Cw₁ = 1; wₙ = 3wₙ₋₁ + 3ⁿ⁻¹

Dw₁ = 0; wₙ = 3wₙ₋₁ + 3ⁿ⁻¹

Solution & Explanation:Because 3wₙ₋₁ = 3(n−2)·3ⁿ⁻² = (n−2)·3ⁿ⁻¹. Adding 3ⁿ⁻¹ gives (n−1)·3ⁿ⁻¹ = wₙ, and w₁=0.

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Frequently Asked Questions

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QIs this ALG2.182 Sequences as Functions worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard ALG2.182 (Practice questions for Sequences as Functions.).