🧠 Arithmetic & Geometric Sequences: Show Your Thinking (F-BF.A.2)

Paginepagineapp.com

Name:

Date:

Write arithmetic and geometric sequences recursively and explicitly. Solve each problem and show your work.

1. Arithmetic: 10, 19, 28, 37, … Explicit formula and 20th term?

Show your work

2. Geometric: 3, -6, 12, -24, … Explicit formula and 8th term?

Show your work

3. Arithmetic: -6, -3, 0, 3, … Explicit formula and 20th term?

Show your work

4. Geometric: 2, 4, 8, 16, … Explicit formula and 8th term?

Show your work

5. Arithmetic: 14, 11, 8, 5, … Explicit formula and 20th term?

Show your work

6. Geometric: 6, 18, 54, 162, … Explicit formula and 8th term?

Show your work

Explain: How did you solve problem 1? Could you check it another way?

Answer key: 1) aₙ = 10 + 9(n − 1); a₂₀ = 181 · 2) aₙ = 3·(-2)^(n−1); a₈ = -384 · 3) aₙ = -6 + 3(n − 1); a₂₀ = 51 · 4) aₙ = 2·(2)^(n−1); a₈ = 256 · 5) aₙ = 14 + -3(n − 1); a₂₀ = -43 · 6) aₙ = 6·(3)^(n−1); a₈ = 13,122

Love free resources? The free Pagine app tracks the books your child reads — kids earn streaks & badges. 📚 App Store · Google Play

← All worksheets

Free to print & share · pagineapp@mwamb.compagineapp.com

Worksheets › Grade 11 Math (Algebra II) › Arithmetic & Geometric Sequences › Arithmetic & Geometric Sequences

Grade 11 (ages 16–17)Numbers & mathsFree printable PDF

About this grade 11 worksheet

Free Grade 11 Algebra II math worksheet (Common Core F-BF.A.2): arithmetic & geometric sequences — problems with space to show work and explain reasoning, with answer key. Skill: Write arithmetic and geometric sequences recursively and explicitly. Level: Grade 11 — also suits Year 12 (UK).

For teachers: skills & standards

CCSS F-BF.A.2: Write arithmetic and geometric sequences recursively and explicitly
Works as a morning-work page, a centre/station activity, homework or an early-finisher task.

Frequently asked questions

Is this worksheet free?

Yes — it is free to print for home or the classroom. Sign in with a free Pagine account, then use the Print button or save it as a PDF.

What age is it for?

It is designed for Grade 11 (ages 16–17), but use it with any child who is ready.

What skills does it build?

Write arithmetic and geometric sequences recursively and explicitly.

Where can I find grade 11 books to read with it?

Pagine's free library has 20,000+ children's books you can read in the Pagine e-reader or the free Pagine app — sorted by age and grade, with free audiobooks too.

More “Arithmetic & Geometric Sequences” printables (f-bf.a.2: write arithmetic and geometric sequences recursively and explicitly)

Arithmetic & Geometric Sequences: Practice A (F-BF.A.2) · Arithmetic & Geometric Sequences: Practice B (F-BF.A.2) · Arithmetic & Geometric Sequences: Mixed Practice & Reasoning (F-BF.A.2) · Arithmetic & Geometric Sequences: Quick Check (F-BF.A.2)

All 5 arithmetic & geometric sequences sheets → · Grade 11 Math (Algebra II): all 10 skills → · All Common Core grades

📚 Read along: 20,000+ free books in the Pagine e-reader

Pair this grade 11 worksheet with a story. Pagine's free library has 20,000+ children's books — classic novels, drama, poetry and non-fiction, classics and free audiobooks — that you can read right in the Pagine e-reader on any phone, tablet or computer, with adjustable text size and night mode. No ads.

Browse free grade 11 books → · Grade 11 reading level · Free audiobooks · High school reading list

📱 Get the free Pagine app — log every book your child reads (scan the barcode or search), set reading goals, and watch streaks and badges grow. Download on the App Store · Get it on Google Play