Precalculus arithmetic series worksheet

In Precalculus arithmetic series are usually written in sigma notation, so the first job is reading the notation: the first term, the last term and how many terms the index runs through. The sum is still the average of the ends times the number of terms.

Also taught in Algebra 2, at its own level and with its own examples.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Arithmetic Series Date Period Find each sum. Find the sum of the first 13 terms: $9, 18, 27, \dots$ Find the sum: $8 + 12 + 16 + \dots + 124$ Find the sum of the first 10 terms: $- 12, - 19, - 26, \dots$ Find the sum: $- 9 - 5 - 1 + \dots + 91$ Find the sum of the first 20 terms: $- 13, - 4, 5, \dots$ Find the sum: $- 4 - 2 + 0 + \dots + 40$ Find the sum of the first 12 terms: $10, 3, - 4, \dots$ Find the sum: $- 2 + 1 + 4 + \dots + 61$ Find the sum of the first 19 terms: $14, 8, 2, \dots$ Find the sum: $12 + 17 + 22 + \dots + 97$ Find the sum of the first 19 terms: $- 12, - 19, - 26, \dots$ Find the sum: $- 5 - 2 + 1 + \dots + 76$ Find the sum of the first 16 terms: $- 14, - 5, 4, \dots$ Find the sum: $- 2 + 0 + 2 + \dots + 20$ Find the sum of the first 18 terms: $9, 1, - 7, \dots$ Find the sum: $- 10 - 8 - 6 + \dots + 28$ Find the sum of the first 20 terms: $13, 20, 27, \dots$ Find the sum: $- 9 - 4 + 1 + \dots + 51$ Find the sum of the first 24 terms: $10, 2, - 6, \dots$ Find the sum: $15 + 19 + 23 + \dots + 99$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic Series

Date Period

Find each sum.

Find the sum of the first 13 terms: $9, 18, 27, \dots$
Find the sum: $8 + 12 + 16 + \dots + 124$
Find the sum of the first 10 terms: $- 12, - 19, - 26, \dots$
Find the sum: $- 9 - 5 - 1 + \dots + 91$
Find the sum of the first 20 terms: $- 13, - 4, 5, \dots$
Find the sum: $- 4 - 2 + 0 + \dots + 40$
Find the sum of the first 12 terms: $10, 3, - 4, \dots$
Find the sum: $- 2 + 1 + 4 + \dots + 61$
Find the sum of the first 19 terms: $14, 8, 2, \dots$
Find the sum: $12 + 17 + 22 + \dots + 97$
Find the sum of the first 19 terms: $- 12, - 19, - 26, \dots$
Find the sum: $- 5 - 2 + 1 + \dots + 76$
Find the sum of the first 16 terms: $- 14, - 5, 4, \dots$
Find the sum: $- 2 + 0 + 2 + \dots + 20$
Find the sum of the first 18 terms: $9, 1, - 7, \dots$
Find the sum: $- 10 - 8 - 6 + \dots + 28$
Find the sum of the first 20 terms: $13, 20, 27, \dots$
Find the sum: $- 9 - 4 + 1 + \dots + 51$
Find the sum of the first 24 terms: $10, 2, - 6, \dots$
Find the sum: $15 + 19 + 23 + \dots + 99$



Sigma Prep · sigmaprep.io/worksheets Name Arithmetic SeriesAnswer keyVersion 1 Date Period Find each sum. Find the sum of the first 13 terms: $9, 18, 27, \dots$ $819$ Find the sum: $8 + 12 + 16 + \dots + 124$ $1980$ Find the sum of the first 10 terms: $- 12, - 19, - 26, \dots$ $- 435$ Find the sum: $- 9 - 5 - 1 + \dots + 91$ $1066$ Find the sum of the first 20 terms: $- 13, - 4, 5, \dots$ $1450$ Find the sum: $- 4 - 2 + 0 + \dots + 40$ $414$ Find the sum of the first 12 terms: $10, 3, - 4, \dots$ $- 342$ Find the sum: $- 2 + 1 + 4 + \dots + 61$ $649$ Find the sum of the first 19 terms: $14, 8, 2, \dots$ $- 760$ Find the sum: $12 + 17 + 22 + \dots + 97$ $981$ Find the sum of the first 19 terms: $- 12, - 19, - 26, \dots$ $- 1425$ Find the sum: $- 5 - 2 + 1 + \dots + 76$ $994$ Find the sum of the first 16 terms: $- 14, - 5, 4, \dots$ $856$ Find the sum: $- 2 + 0 + 2 + \dots + 20$ $108$ Find the sum of the first 18 terms: $9, 1, - 7, \dots$ $- 1062$ Find the sum: $- 10 - 8 - 6 + \dots + 28$ $180$ Find the sum of the first 20 terms: $13, 20, 27, \dots$ $1590$ Find the sum: $- 9 - 4 + 1 + \dots + 51$ $273$ Find the sum of the first 24 terms: $10, 2, - 6, \dots$ $- 1968$ Find the sum: $15 + 19 + 23 + \dots + 99$ $1254$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic SeriesAnswer keyVersion 1

Date Period

Find each sum.

Find the sum of the first 13 terms: $9, 18, 27, \dots$ $819$
Find the sum: $8 + 12 + 16 + \dots + 124$ $1980$
Find the sum of the first 10 terms: $- 12, - 19, - 26, \dots$ $- 435$
Find the sum: $- 9 - 5 - 1 + \dots + 91$ $1066$
Find the sum of the first 20 terms: $- 13, - 4, 5, \dots$ $1450$
Find the sum: $- 4 - 2 + 0 + \dots + 40$ $414$
Find the sum of the first 12 terms: $10, 3, - 4, \dots$ $- 342$
Find the sum: $- 2 + 1 + 4 + \dots + 61$ $649$
Find the sum of the first 19 terms: $14, 8, 2, \dots$ $- 760$
Find the sum: $12 + 17 + 22 + \dots + 97$ $981$
Find the sum of the first 19 terms: $- 12, - 19, - 26, \dots$ $- 1425$
Find the sum: $- 5 - 2 + 1 + \dots + 76$ $994$
Find the sum of the first 16 terms: $- 14, - 5, 4, \dots$ $856$
Find the sum: $- 2 + 0 + 2 + \dots + 20$ $108$
Find the sum of the first 18 terms: $9, 1, - 7, \dots$ $- 1062$
Find the sum: $- 10 - 8 - 6 + \dots + 28$ $180$
Find the sum of the first 20 terms: $13, 20, 27, \dots$ $1590$
Find the sum: $- 9 - 4 + 1 + \dots + 51$ $273$
Find the sum of the first 24 terms: $10, 2, - 6, \dots$ $- 1968$
Find the sum: $15 + 19 + 23 + \dots + 99$ $1254$

How to do these

$\sum_{k = 1}^{20} (3 k - 2)$

First term: k = 1 gives 1. Last term: k = 20 gives 58.
The index runs from 1 to 20, so there are 20 terms.
Sum: 20(1 + 58)/2 = 10 × 59.

The answer is $590$ .

Where students go wrong

Miscounting the terms when the index does not start at 1. From k = 3 to k = 20 there are 20 - 3 + 1 = 18 terms, not 17.

Also called sum of an arithmetic sequence, sigma notation or partial sums.

What you can put on this worksheet

The sum of an arithmetic series: Find the sum of the first 7 terms: $5, 6, 7, \dots$ → $56$
Given the last term: Find the sum: $3 + 7 + 11 + \dots + 51$ → $351$
Big sigma, S from the ends, finding n: Find $n$ :
$a_{1} = 44, a_{n} = - 70, S_{n} = - 260$ → $n = 20$

Questions about these worksheets

Yes. Every arithmetic series 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 series 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 three 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: the sum of an arithmetic series, given the last term and big sigma, s from the ends, finding n. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the last term you were shown instead of the last term you are summing to. The formula needs the nth term, and on a sheet like this it is usually one you have to work out first.

Precalculus arithmetic series worksheet

Arithmetic Series

Arithmetic SeriesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these arithmetic series worksheets free?+

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

Are these arithmetic series worksheets printable?+

What grade are these arithmetic series worksheets for?+

Can I get a different version of the same arithmetic series worksheet?+

Is this a free alternative to Kuta Software for arithmetic series?+

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What do students get wrong with arithmetic series?+