Free Printable WorksheetMathAlgebra IMath CurriculumF-IF.3

ALG1.118 Find Terms and Parameters from Representations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.118 Find Terms and Parameters from Representations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.118 Find Terms and Parameters from Representations - Identify the first term, common difference, or common ratio from a table, graph, or formula; Select the option that shows how to use those parameters to generate additional terms. (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 ALG1.118 Find Terms and Parameters from Representations skill assessments:

Problem 1Difficulty: Mastery
The sequence 12, 18, 27, ... is geometric. Which option correctly uses the parameters to find a_5?
Aa_1 = 12, r = 1.5, so a_5 = 12(1.5)4 = 60.75
Ba_1 = 12, d = 6, so a_5 = 36
Ca_1 = 18, r = 1.5, so a_5 = 18(1.5)5 = 136.6875
Da_1 = 12, r = 6, so a_5 = 15552
Solution & Explanation:The first term is 12 and the common ratio is 18 / 12 = 1.5. Term 5 is 4 ratio steps after term 1, so a_5 = 12(1.5)4 = 60.75.
Problem 2Difficulty: Mastery
Which recursive description matches the explicit formula a_n = 3 - 6(n - 1)?
Aa_1 = 3; subtract 6 each time
Ba_1 = -3; subtract 6 each time
Ca_1 = 3; multiply by -6 each time
Da_1 = 6; add 3 each time
Solution & Explanation:The explicit formula is arithmetic with a_1 = 3 and d = -6. A recursive description is to start at 3 and subtract 6 each time.
Problem 3Difficulty: Mastery
Two sequences are shown. Sequence X: n: 1, 2, 3, 4; X_n: 5, 9, 13, 17. Sequence Y: n: 1, 2, 3, 4; Y_n: 5, 10, 20, 40. Which comparison is correct?
ABoth are arithmetic with common difference 4.
BBoth are geometric with common ratio 2.
CThey have the same first term; X has common difference 4 and Y has common ratio 2.
DThey have different first terms; X has common ratio 4 and Y has common difference 5.
Solution & Explanation:Both sequences start at 5. X adds 4 each time, while Y multiplies by 2 each time.

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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: Identify the first term, common difference, or common ratio from a table, graph, or formula; Select the option that shows how to use those parameters to generate additional terms. 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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