Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.3

Pre CAL.153 Determine the nth Term from a Pattern or Table Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.153 Determine the nth Term from a Pattern or Table. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.153 Determine the nth Term from a Pattern or Table - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.3. Skill statement in this prompt cell: Given a sequence pattern or table, determine the explicit formula for the nth term and select the correct expression. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.3; CCSS HSF-BF.2; CCSS HSF-LE.2; CCSS HSA-APR.5(+); SMP 1,2,4,7,8; AP Precalculus CED Unit 2; TX §111.42(c)(5)(A); FL MA.912.AR.10.1-10.5; VA MA.FR.3. Use this prompt-provided wording as the supporting standard description for this workflow.

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

Pre-Calculus

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 Pre CAL.153 Determine the nth Term from a Pattern or Table skill assessments:

Problem 1Difficulty: Mastery
The pattern lists a_1 through a_4 as 1, 3, 8, 17. What is the explicit rule for a_n?
Aa_n = n2 + 2n
Ba_n = (n - 1)2 + 2n
Ca_n = (n + 1)2 + 2^(n-1)
Da_n = (n - 1)2 + 2^(n-1)
Solution & Explanation:Both parts are indexed from n=1, so the exponent and square each use n - 1. Substituting into a_n = (n - 1)2 + 2^(n-1) confirms the table: n=1 gives 1; n=2 gives 3; n=3 gives 8; n=4 gives 17.
Problem 2Difficulty: Mastery
For the sequence table n | 1|2|3|4; a_n | 5|13|35|97, choose the explicit nth-term expression.
Aa_n = 5n
Ba_n = 2^(n+1) + 3^(n-1)
Ca_n = 2n + 3n
Da_n = n2 + 3n
Solution & Explanation:Each output is the sum of a power of 2 and a power of 3. Substituting into a_n = 2n + 3n confirms the table: n=1 gives 5; n=2 gives 13; n=3 gives 35; n=4 gives 97.
Problem 3Difficulty: Mastery
A sequence begins 1, 3, 12, 60 for n = 1 to 4. Select the nth-term formula.
Aa_n = n!/2
Ba_n = (n + 1)!/2
Ca_n = (n + 1)!
Da_n = 2(n + 1)!
Solution & Explanation:The terms grow factorially rather than by a fixed difference or ratio. Substituting into a_n = (n + 1)!/2 confirms the table: n=1 gives 1; n=2 gives 3; n=3 gives 12; n=4 gives 60.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSF-IF.3 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.3. Skill statement in this prompt cell: Given a sequence pattern or table, determine the explicit formula for the nth term and select the correct expression. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.3; CCSS HSF-BF.2; CCSS HSF-LE.2; CCSS HSA-APR.5(+); SMP 1,2,4,7,8; AP Precalculus CED Unit 2; TX §111.42(c)(5)(A); FL MA.912.AR.10.1-10.5; VA MA.FR.3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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