Precalculus arithmetic and geometric sequences worksheet

Arithmetic sequences add the same amount each time, geometric ones multiply. Tick both and students have to work out which is which before they can start.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Sequences Date Period Answer each question. Find the 47th term: $21, 41, 61, 81, \dots$ Find a formula for the nth term: $- 95, - 126, - 157, - 188, \dots$ Find the 8th term: $- 11, 33, - 99, 297, \dots$ Which term of $25, 12, - 1, - 14, \dots$ is $- 651$ ? Find a formula for the nth term: $- 76, - 39, - 2, 35, \dots$ Find the 9th term: $- 12, 24, - 48, 96, \dots$ Which term of $- 25, - 39, - 53, - 67, \dots$ is $- 641$ ? Find a formula for the nth term: $- 42, - 3, 36, 75, \dots$ Find the 11th term: $- 12, - 36, - 108, - 324, \dots$ Find the 26th term: $31, 50, 69, 88, \dots$ Find a formula for the nth term: $- 89, - 48, - 7, 34, \dots$ Which term of $10, 30, 90, 270, \dots$ is $1771470$ ? Which term of $- 22, - 37, - 52, - 67, \dots$ is $- 667$ ? Find a formula for the nth term: $87, 64, 41, 18, \dots$ Which term of $- 12, 36, - 108, 324, \dots$ is $236196$ ? Find the 29th term: $- 23, - 38, - 53, - 68, \dots$ Find a formula for the nth term: $51, 76, 101, 126, \dots$ Find the 8th term: $12, 48, 192, 768, \dots$ Find the 53rd term: $- 31, - 18, - 5, 8, \dots$ Find a formula for the nth term: $- 45, - 74, - 103, - 132, \dots$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Sequences

Date Period

Answer each question.

Find the 47th term: $21, 41, 61, 81, \dots$
Find a formula for the nth term: $- 95, - 126, - 157, - 188, \dots$
Find the 8th term: $- 11, 33, - 99, 297, \dots$
Which term of $25, 12, - 1, - 14, \dots$ is $- 651$ ?
Find a formula for the nth term: $- 76, - 39, - 2, 35, \dots$
Find the 9th term: $- 12, 24, - 48, 96, \dots$
Which term of $- 25, - 39, - 53, - 67, \dots$ is $- 641$ ?
Find a formula for the nth term: $- 42, - 3, 36, 75, \dots$
Find the 11th term: $- 12, - 36, - 108, - 324, \dots$
Find the 26th term: $31, 50, 69, 88, \dots$
Find a formula for the nth term: $- 89, - 48, - 7, 34, \dots$
Which term of $10, 30, 90, 270, \dots$ is $1771470$ ?
Which term of $- 22, - 37, - 52, - 67, \dots$ is $- 667$ ?
Find a formula for the nth term: $87, 64, 41, 18, \dots$
Which term of $- 12, 36, - 108, 324, \dots$ is $236196$ ?
Find the 29th term: $- 23, - 38, - 53, - 68, \dots$
Find a formula for the nth term: $51, 76, 101, 126, \dots$
Find the 8th term: $12, 48, 192, 768, \dots$
Find the 53rd term: $- 31, - 18, - 5, 8, \dots$
Find a formula for the nth term: $- 45, - 74, - 103, - 132, \dots$



Sigma Prep · sigmaprep.io/worksheets Name SequencesAnswer keyVersion 1 Date Period Answer each question. Find the 47th term: $21, 41, 61, 81, \dots$ $941$ Find a formula for the nth term: $- 95, - 126, - 157, - 188, \dots$ $a_{n} = - 31 n - 64$ Find the 8th term: $- 11, 33, - 99, 297, \dots$ $24057$ Which term of $25, 12, - 1, - 14, \dots$ is $- 651$ ? $53$ Find a formula for the nth term: $- 76, - 39, - 2, 35, \dots$ $a_{n} = 37 n - 113$ Find the 9th term: $- 12, 24, - 48, 96, \dots$ $- 3072$ Which term of $- 25, - 39, - 53, - 67, \dots$ is $- 641$ ? $45$ Find a formula for the nth term: $- 42, - 3, 36, 75, \dots$ $a_{n} = 39 n - 81$ Find the 11th term: $- 12, - 36, - 108, - 324, \dots$ $- 708588$ Find the 26th term: $31, 50, 69, 88, \dots$ $506$ Find a formula for the nth term: $- 89, - 48, - 7, 34, \dots$ $a_{n} = 41 n - 130$ Which term of $10, 30, 90, 270, \dots$ is $1771470$ ? $12$ Which term of $- 22, - 37, - 52, - 67, \dots$ is $- 667$ ? $44$ Find a formula for the nth term: $87, 64, 41, 18, \dots$ $a_{n} = - 23 n + 110$ Which term of $- 12, 36, - 108, 324, \dots$ is $236196$ ? $10$ Find the 29th term: $- 23, - 38, - 53, - 68, \dots$ $- 443$ Find a formula for the nth term: $51, 76, 101, 126, \dots$ $a_{n} = 25 n + 26$ Find the 8th term: $12, 48, 192, 768, \dots$ $196608$ Find the 53rd term: $- 31, - 18, - 5, 8, \dots$ $645$ Find a formula for the nth term: $- 45, - 74, - 103, - 132, \dots$ $a_{n} = - 29 n - 16$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

SequencesAnswer keyVersion 1

Date Period

Answer each question.

Find the 47th term: $21, 41, 61, 81, \dots$ $941$
Find a formula for the nth term: $- 95, - 126, - 157, - 188, \dots$ $a_{n} = - 31 n - 64$
Find the 8th term: $- 11, 33, - 99, 297, \dots$ $24057$
Which term of $25, 12, - 1, - 14, \dots$ is $- 651$ ? $53$
Find a formula for the nth term: $- 76, - 39, - 2, 35, \dots$ $a_{n} = 37 n - 113$
Find the 9th term: $- 12, 24, - 48, 96, \dots$ $- 3072$
Which term of $- 25, - 39, - 53, - 67, \dots$ is $- 641$ ? $45$
Find a formula for the nth term: $- 42, - 3, 36, 75, \dots$ $a_{n} = 39 n - 81$
Find the 11th term: $- 12, - 36, - 108, - 324, \dots$ $- 708588$
Find the 26th term: $31, 50, 69, 88, \dots$ $506$
Find a formula for the nth term: $- 89, - 48, - 7, 34, \dots$ $a_{n} = 41 n - 130$
Which term of $10, 30, 90, 270, \dots$ is $1771470$ ? $12$
Which term of $- 22, - 37, - 52, - 67, \dots$ is $- 667$ ? $44$
Find a formula for the nth term: $87, 64, 41, 18, \dots$ $a_{n} = - 23 n + 110$
Which term of $- 12, 36, - 108, 324, \dots$ is $236196$ ? $10$
Find the 29th term: $- 23, - 38, - 53, - 68, \dots$ $- 443$
Find a formula for the nth term: $51, 76, 101, 126, \dots$ $a_{n} = 25 n + 26$
Find the 8th term: $12, 48, 192, 768, \dots$ $196608$
Find the 53rd term: $- 31, - 18, - 5, 8, \dots$ $645$
Find a formula for the nth term: $- 45, - 74, - 103, - 132, \dots$ $a_{n} = - 29 n - 16$

How to do these

Find the 20th term: $3, 7, 11, 15, \dots$

It goes up by 4 each time, so it is arithmetic.
The 20th term is 19 steps after the first.
3 + 19 × 4.

The answer is $79$ .

Where students go wrong

Multiplying by the term number instead of one less than it. Getting to the 20th term takes 19 steps, not 20, which is the off-by-one that costs most of the marks on this topic.

Also called the nth term, explicit formulas or number patterns.

What you can put on this worksheet

A given term of an arithmetic sequence: Find the 9th term: $6, 7, 8, 9, \dots$ → $14$
A formula for an arithmetic sequence: Find a formula for the nth term: $6, 7, 8, 9, \dots$ → $a_{n} = n + 5$
A given term of a geometric sequence: Find the 5th term: $3, 9, 27, 81, \dots$ → $243$

Questions about these worksheets

Yes. Every arithmetic and geometric sequences sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the arithmetic and geometric sequences questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: a given term of an arithmetic sequence, a formula for an arithmetic sequence and a given term of a geometric sequence. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying by the term number instead of one less than it. Getting to the 20th term takes 19 steps, not 20, which is the off-by-one that costs most of the marks on this topic.

Precalculus arithmetic and geometric sequences worksheet

Select your difficulty

Sequences

SequencesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these arithmetic and geometric sequences worksheets free?+

Do the arithmetic and geometric sequences worksheets come with an answer key?+

Are these arithmetic and geometric sequences worksheets printable?+

What grade are these arithmetic and geometric sequences worksheets for?+

Can I get a different version of the same arithmetic and geometric sequences worksheet?+

Is this a free alternative to Kuta Software for arithmetic and geometric sequences?+

Can I choose how hard the arithmetic and geometric sequences questions are?+

What kinds of question are on a arithmetic and geometric sequences worksheet?+

What do students get wrong with arithmetic and geometric sequences?+