Free Printable WorksheetMathAlgebra IMath CurriculumF-IF.3

ALG1.117 Convert Between Explicit and Recursive Forms Answer Key Worksheet

Download our free printable Algebra I Math worksheet on ALG1.117 Convert Between Explicit and Recursive Forms Answer Key. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Convert Between Explicit and Recursive Forms Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.117 Convert Between Explicit and Recursive Forms Answer Key. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.117 Convert Between Explicit and Recursive Forms - Select the form that correctly converts between explicit and recursive definitions when possible; Select the explanation that correctly explains how the difference or ratio is represented in each form. (CCSS: F-IF.3; F-BF.2; TEKS: §111.39(c)(10) (sequences referenced), local scope; VA SOL: A.F.2 g (comparisons); FL B.E.S.T.: MA.912.F.1.1 (function types include linear/exponential), MA.912.AR.5.* (geometric growth); NY-NGLS: AI-F.IF.3, AI-F.BF.2; CA CCSSM: F-IF.3, F-BF.2; MA 2017: HS.F-BF.2; DoDEA CCRSM; NAEP: Algebra—patterns; NCTM P2A: Practices 2, 4.)

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 I

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 ALG1.117 Convert Between Explicit and Recursive Forms Answer Key skill assessments:

Problem 1Difficulty: Mastery

For n >= 1, the explicit formula is a_n = 6 + 2(n - 1), and the recursive definition is a_1 = 6 and a_n = a_(n-1) + 2. Which explanation best proves they are equivalent?

ABoth forms use the same first term 6 and the same constant difference 2, so they generate the same arithmetic sequence.

BThey are equivalent because both contain the number 6 somewhere.

CThey are not equivalent because one form uses n - 1 and the other does not.

DThey are equivalent only for n = 2 because the recursive form starts later.

Solution & Explanation:For arithmetic sequences, matching the first term and common difference is enough to show the explicit and recursive forms define the same sequence.

Problem 2Difficulty: Mastery

The terms are -1, 2, -4, 8. Which pair of definitions correctly represents the sequence for n >= 1?

Aa_n = -1 + 3(n - 1); a_1 = -1 and a_n = a_(n-1) + 3

Ba_n = -1*(-2)^(n - 1); a_1 = -1 and a_n = -2a_(n-1)

Ca_n = 2*(-2)^(n - 1); a_1 = 2 and a_n = -2a_(n-1)

Da_n = -1*2^(n - 1); a_1 = -1 and a_n = 2a_(n-1)

Solution & Explanation:Each term is -2 times the previous term. The first term is -1, so the explicit formula is -1*(-2)^(n - 1).

Problem 3Difficulty: Mastery

A sequence has recursive definition s_1 = 2/3 and s_n = s_(n-1) + 1/6 for n >= 2. Which explicit formula is equivalent?

As_n = 2/3 + (1/6)(n - 1)

Bs_n = 1/6 + (2/3)(n - 1)

Cs_n = (2/3)*(1/6)^(n - 1)

Ds_n = 2/3 + (1/6)n

Solution & Explanation:The recursive rule is arithmetic with first term 2/3 and common difference 1/6, so use s_n = 2/3 + (1/6)(n - 1).

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this ALG1.117 Convert Between Explicit and Recursive Forms Answer Key worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this ALG1.117 Convert Between Explicit and Recursive Forms Answer Key worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice ALG1.117 Convert Between Explicit and Recursive Forms Answer Key online with instant feedback?

Yes! In addition to this printable worksheet, students can practice ALG1.117 Convert Between Explicit and Recursive Forms Answer Key interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard F-IF.3 (Students convert between explicit and recursive definitions of arithmetic and geometric sequences when possible and explain how the difference or ratio is represented in each form. Associated standards include CCSS F-IF.3 and F-BF.2, with related state and local sequence/function standards as applicable.).