Precalculus arithmetic sequences worksheet

The same amount is added each step, so getting to the nth term takes n minus one steps. That off-by-one is most of the marks on this topic.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Arithmetic 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 39th term: $- 27, - 41, - 55, - 69, \dots$ Find a formula for the nth term: $- 50, - 79, - 108, - 137, \dots$ Which term of $32, 18, 4, - 10, \dots$ is $- 682$ ? Find a formula for the nth term: $65, 107, 149, 191, \dots$ Find the 30th term: $- 32, - 47, - 62, - 77, \dots$ Find a formula for the nth term: $47, 26, 5, - 16, \dots$ Find the 35th term: $33, 13, - 7, - 27, \dots$ Find a formula for the nth term: $91, 132, 173, 214, \dots$ Find the 56th term: $35, 22, 9, - 4, \dots$ Find a formula for the nth term: $79, 44, 9, - 26, \dots$ Which term of $22, 36, 50, 64, \dots$ is $554$ ? Find a formula for the nth term: $68, 89, 110, 131, \dots$ Which term of $33, 19, 5, - 9, \dots$ is $- 443$ ? Find a formula for the nth term: $70, 48, 26, 4, \dots$ Find the 43rd term: $- 22, - 40, - 58, - 76, \dots$ Find a formula for the nth term: $- 84, - 126, - 168, - 210, \dots$ Find the 36th term: $34, 20, 6, - 8, \dots$ Find a formula for the nth term: $45, 5, - 35, - 75, \dots$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic 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 39th term: $- 27, - 41, - 55, - 69, \dots$
Find a formula for the nth term: $- 50, - 79, - 108, - 137, \dots$
Which term of $32, 18, 4, - 10, \dots$ is $- 682$ ?
Find a formula for the nth term: $65, 107, 149, 191, \dots$
Find the 30th term: $- 32, - 47, - 62, - 77, \dots$
Find a formula for the nth term: $47, 26, 5, - 16, \dots$
Find the 35th term: $33, 13, - 7, - 27, \dots$
Find a formula for the nth term: $91, 132, 173, 214, \dots$
Find the 56th term: $35, 22, 9, - 4, \dots$
Find a formula for the nth term: $79, 44, 9, - 26, \dots$
Which term of $22, 36, 50, 64, \dots$ is $554$ ?
Find a formula for the nth term: $68, 89, 110, 131, \dots$
Which term of $33, 19, 5, - 9, \dots$ is $- 443$ ?
Find a formula for the nth term: $70, 48, 26, 4, \dots$
Find the 43rd term: $- 22, - 40, - 58, - 76, \dots$
Find a formula for the nth term: $- 84, - 126, - 168, - 210, \dots$
Find the 36th term: $34, 20, 6, - 8, \dots$
Find a formula for the nth term: $45, 5, - 35, - 75, \dots$



Sigma Prep · sigmaprep.io/worksheets Name Arithmetic 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 39th term: $- 27, - 41, - 55, - 69, \dots$ $- 559$ Find a formula for the nth term: $- 50, - 79, - 108, - 137, \dots$ $a_{n} = - 29 n - 21$ Which term of $32, 18, 4, - 10, \dots$ is $- 682$ ? $52$ Find a formula for the nth term: $65, 107, 149, 191, \dots$ $a_{n} = 42 n + 23$ Find the 30th term: $- 32, - 47, - 62, - 77, \dots$ $- 467$ Find a formula for the nth term: $47, 26, 5, - 16, \dots$ $a_{n} = - 21 n + 68$ Find the 35th term: $33, 13, - 7, - 27, \dots$ $- 647$ Find a formula for the nth term: $91, 132, 173, 214, \dots$ $a_{n} = 41 n + 50$ Find the 56th term: $35, 22, 9, - 4, \dots$ $- 680$ Find a formula for the nth term: $79, 44, 9, - 26, \dots$ $a_{n} = - 35 n + 114$ Which term of $22, 36, 50, 64, \dots$ is $554$ ? $39$ Find a formula for the nth term: $68, 89, 110, 131, \dots$ $a_{n} = 21 n + 47$ Which term of $33, 19, 5, - 9, \dots$ is $- 443$ ? $35$ Find a formula for the nth term: $70, 48, 26, 4, \dots$ $a_{n} = - 22 n + 92$ Find the 43rd term: $- 22, - 40, - 58, - 76, \dots$ $- 778$ Find a formula for the nth term: $- 84, - 126, - 168, - 210, \dots$ $a_{n} = - 42 n - 42$ Find the 36th term: $34, 20, 6, - 8, \dots$ $- 456$ Find a formula for the nth term: $45, 5, - 35, - 75, \dots$ $a_{n} = - 40 n + 85$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic 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 39th term: $- 27, - 41, - 55, - 69, \dots$ $- 559$
Find a formula for the nth term: $- 50, - 79, - 108, - 137, \dots$ $a_{n} = - 29 n - 21$
Which term of $32, 18, 4, - 10, \dots$ is $- 682$ ? $52$
Find a formula for the nth term: $65, 107, 149, 191, \dots$ $a_{n} = 42 n + 23$
Find the 30th term: $- 32, - 47, - 62, - 77, \dots$ $- 467$
Find a formula for the nth term: $47, 26, 5, - 16, \dots$ $a_{n} = - 21 n + 68$
Find the 35th term: $33, 13, - 7, - 27, \dots$ $- 647$
Find a formula for the nth term: $91, 132, 173, 214, \dots$ $a_{n} = 41 n + 50$
Find the 56th term: $35, 22, 9, - 4, \dots$ $- 680$
Find a formula for the nth term: $79, 44, 9, - 26, \dots$ $a_{n} = - 35 n + 114$
Which term of $22, 36, 50, 64, \dots$ is $554$ ? $39$
Find a formula for the nth term: $68, 89, 110, 131, \dots$ $a_{n} = 21 n + 47$
Which term of $33, 19, 5, - 9, \dots$ is $- 443$ ? $35$
Find a formula for the nth term: $70, 48, 26, 4, \dots$ $a_{n} = - 22 n + 92$
Find the 43rd term: $- 22, - 40, - 58, - 76, \dots$ $- 778$
Find a formula for the nth term: $- 84, - 126, - 168, - 210, \dots$ $a_{n} = - 42 n - 42$
Find the 36th term: $34, 20, 6, - 8, \dots$ $- 456$
Find a formula for the nth term: $45, 5, - 35, - 75, \dots$ $a_{n} = - 40 n + 85$

How to do these

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

It goes up by 4 each time.
The 20th term is 19 steps after the first.
3 plus 19 times 4.

The answer is $79$ .

Where students go wrong

Multiplying by the term number rather than one less. Reaching the 20th term takes 19 steps, not 20.

Also called common difference, nth term of an arithmetic sequence or explicit formula.

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: $6, 7, 8, 9, \dots$ → $a_{n} = n + 5$
Insert arithmetic means: Insert 2 arithmetic means between $1$ and $- 8$ → $- 2, - 5$

Questions about these worksheets

Yes. Every arithmetic 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 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 insert arithmetic means. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying by the term number rather than one less. Reaching the 20th term takes 19 steps, not 20.

Precalculus arithmetic sequences worksheet

Select your difficulty

Arithmetic Sequences

Arithmetic 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 sequences worksheets free?+

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

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