Free Printable WorksheetMathAlgebra IMath CurriculumF-IF.3

ALG1.115 Explicit and Recursive Sequence Rules Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.115 Explicit and Recursive Sequence Rules. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.115 Explicit and Recursive Sequence Rules - Select the equation, inequality, expression, or function that represents explicit and recursive rules for arithmetic and geometric sequences; Select the correct value of terms using the rule and explain what the term number represents. (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 ALG1.115 Explicit and Recursive Sequence Rules skill assessments:

Problem 1Difficulty: Mastery
A file download model has d_1 = 50 MB and d_n = 1.2d_(n - 1) for n >= 2. Which explicit rule and fourth term are correct?
Ad_n = 50(1.2)^(n - 1); d_4 = 86.4
Bd_n = 50(1.2)n; d_4 = 103.68
Cd_n = 50 + 1.2(n - 1); d_4 = 53.6
Dd_n = 1.2(50)^(n - 1); d_4 = 150000
Solution & Explanation:The recursive rule multiplies by 1.2, so the explicit rule is d_n = 50(1.2)^(n - 1). Then d_4 = 50(1.2)3 = 86.4.
Problem 2Difficulty: Mastery
Sequence A is A_n = 3n. Sequence G is G_n = 3 * 2^(n - 1). For which positive term numbers do the sequences have the same value?
An = 1 only
Bn = 2 only
Cn = 1 and n = 2
DThey never have the same value
Solution & Explanation:Compare values: at n = 1, both are 3; at n = 2, both are 6. After that, G_n grows faster: 12, 24, ... while A_n is 9, 12, ....
Problem 3Difficulty: Mastery
An arithmetic sequence can be represented by a linear function whose domain is the positive integers.
ATrue
BFalse
Solution & Explanation:An arithmetic sequence has a constant difference, so its explicit rule has the form a_n = a_1 + d(n - 1), which is linear when restricted to positive integer inputs.

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Frequently Asked Questions

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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 (Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.3. Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents explicit and recursive rules for arithmetic and geometric sequences; Select the correct value of terms using the rule and explain what the term number represents. Associated standards listed with this skill in the curriculum source: 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. Use this prompt-provided wording as the supporting standard description for this workflow.).

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