Arithmetic and geometric series worksheet for Algebra 2

A series is a sequence added up. The arithmetic formula is really just the average term times how many there are, which is worth saying out loud because it makes the formula memorable rather than magic.

Also taught in Algebra 1 and Precalculus, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Arithmetic Sequences (Algebra 2). Adding the same amount each time.
Sequences (Algebra 2). A term, which term, or a formula for the nth term.
Arithmetic Series (Algebra 2). Adding up a sequence with a constant step.

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



Sigma Prep · sigmaprep.io/worksheets Name Series Date Period Find each sum. Sum an arithmetic series Find the sum of the first 10 terms: $1, 6, 11, \dots$ Find the sum of the first 40 terms: $18, 8, - 2, \dots$ Find the sum of the first 25 terms: $- 9, 0, 9, \dots$ Find the sum of the first 5 terms: $3, - 1, - 5, \dots$ Find the sum of the first 41 terms: $- 19, - 4, 11, \dots$ Find the sum of the first 9 terms: $- 12, - 18, - 24, \dots$ Find the sum of the first 5 terms: $4, 0, - 4, \dots$ Find the sum of the first 37 terms: $- 16, - 6, 4, \dots$ Find the sum of the first 22 terms: $12, 5, - 2, \dots$ Find the sum of the first 10 terms: $- 2, 0, 2, \dots$ Sum a geometric series Find the sum of the first 5 terms: $- 5, 10, - 20, \dots$ Find the sum of the first 5 terms: $- 1, - 3, - 9, \dots$ Find the sum of the first 8 terms: $12, - 48, 192, \dots$ Find the sum of the first 9 terms: $7, - 14, 28, \dots$ Find the sum of the first 4 terms: $1, 2, 4, \dots$ Find the sum of the first 9 terms: $- 10, 30, - 90, \dots$ Find the sum of the first 8 terms: $- 5, - 10, - 20, \dots$ Find the sum of the first 5 terms: $3, 6, 12, \dots$ Find the sum of the first 7 terms: $10, - 40, 160, \dots$ Find the sum of the first 6 terms: $- 7, 14, - 28, \dots$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Series

Date Period

Find each sum.

Sum an arithmetic series
Find the sum of the first 10 terms: $1, 6, 11, \dots$
Find the sum of the first 40 terms: $18, 8, - 2, \dots$
Find the sum of the first 25 terms: $- 9, 0, 9, \dots$
Find the sum of the first 5 terms: $3, - 1, - 5, \dots$
Find the sum of the first 41 terms: $- 19, - 4, 11, \dots$
Find the sum of the first 9 terms: $- 12, - 18, - 24, \dots$
Find the sum of the first 5 terms: $4, 0, - 4, \dots$
Find the sum of the first 37 terms: $- 16, - 6, 4, \dots$
Find the sum of the first 22 terms: $12, 5, - 2, \dots$
Find the sum of the first 10 terms: $- 2, 0, 2, \dots$

Sum a geometric series
Find the sum of the first 5 terms: $- 5, 10, - 20, \dots$
Find the sum of the first 5 terms: $- 1, - 3, - 9, \dots$
Find the sum of the first 8 terms: $12, - 48, 192, \dots$
Find the sum of the first 9 terms: $7, - 14, 28, \dots$
Find the sum of the first 4 terms: $1, 2, 4, \dots$
Find the sum of the first 9 terms: $- 10, 30, - 90, \dots$
Find the sum of the first 8 terms: $- 5, - 10, - 20, \dots$
Find the sum of the first 5 terms: $3, 6, 12, \dots$
Find the sum of the first 7 terms: $10, - 40, 160, \dots$
Find the sum of the first 6 terms: $- 7, 14, - 28, \dots$



Sigma Prep · sigmaprep.io/worksheets Name SeriesAnswer keyVersion 1 Date Period Find each sum. Sum an arithmetic series Find the sum of the first 10 terms: $1, 6, 11, \dots$ $235$ Find the sum of the first 40 terms: $18, 8, - 2, \dots$ $- 7080$ Find the sum of the first 25 terms: $- 9, 0, 9, \dots$ $2475$ Find the sum of the first 5 terms: $3, - 1, - 5, \dots$ $- 25$ Find the sum of the first 41 terms: $- 19, - 4, 11, \dots$ $11521$ Find the sum of the first 9 terms: $- 12, - 18, - 24, \dots$ $- 324$ Find the sum of the first 5 terms: $4, 0, - 4, \dots$ $- 20$ Find the sum of the first 37 terms: $- 16, - 6, 4, \dots$ $6068$ Find the sum of the first 22 terms: $12, 5, - 2, \dots$ $- 1353$ Find the sum of the first 10 terms: $- 2, 0, 2, \dots$ $70$ Sum a geometric series Find the sum of the first 5 terms: $- 5, 10, - 20, \dots$ $- 55$ Find the sum of the first 5 terms: $- 1, - 3, - 9, \dots$ $- 121$ Find the sum of the first 8 terms: $12, - 48, 192, \dots$ $- 157284$ Find the sum of the first 9 terms: $7, - 14, 28, \dots$ $1197$ Find the sum of the first 4 terms: $1, 2, 4, \dots$ $15$ Find the sum of the first 9 terms: $- 10, 30, - 90, \dots$ $- 49210$ Find the sum of the first 8 terms: $- 5, - 10, - 20, \dots$ $- 1275$ Find the sum of the first 5 terms: $3, 6, 12, \dots$ $93$ Find the sum of the first 7 terms: $10, - 40, 160, \dots$ $32770$ Find the sum of the first 6 terms: $- 7, 14, - 28, \dots$ $147$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

SeriesAnswer keyVersion 1

Date Period

Find each sum.

Sum an arithmetic series
Find the sum of the first 10 terms: $1, 6, 11, \dots$ $235$
Find the sum of the first 40 terms: $18, 8, - 2, \dots$ $- 7080$
Find the sum of the first 25 terms: $- 9, 0, 9, \dots$ $2475$
Find the sum of the first 5 terms: $3, - 1, - 5, \dots$ $- 25$
Find the sum of the first 41 terms: $- 19, - 4, 11, \dots$ $11521$
Find the sum of the first 9 terms: $- 12, - 18, - 24, \dots$ $- 324$
Find the sum of the first 5 terms: $4, 0, - 4, \dots$ $- 20$
Find the sum of the first 37 terms: $- 16, - 6, 4, \dots$ $6068$
Find the sum of the first 22 terms: $12, 5, - 2, \dots$ $- 1353$
Find the sum of the first 10 terms: $- 2, 0, 2, \dots$ $70$

Sum a geometric series
Find the sum of the first 5 terms: $- 5, 10, - 20, \dots$ $- 55$
Find the sum of the first 5 terms: $- 1, - 3, - 9, \dots$ $- 121$
Find the sum of the first 8 terms: $12, - 48, 192, \dots$ $- 157284$
Find the sum of the first 9 terms: $7, - 14, 28, \dots$ $1197$
Find the sum of the first 4 terms: $1, 2, 4, \dots$ $15$
Find the sum of the first 9 terms: $- 10, 30, - 90, \dots$ $- 49210$
Find the sum of the first 8 terms: $- 5, - 10, - 20, \dots$ $- 1275$
Find the sum of the first 5 terms: $3, 6, 12, \dots$ $93$
Find the sum of the first 7 terms: $10, - 40, 160, \dots$ $32770$
Find the sum of the first 6 terms: $- 7, 14, - 28, \dots$ $147$

How to do these

Find the sum of the first 20 terms: $3, 7, 11, \dots$

The 20th term is 3 + 19 × 4 = 79.
The average of the first and last is (3 + 79)/2 = 41.
Twenty terms averaging 41.

The answer is $820$ .

Where students go wrong

Using the arithmetic formula on a geometric series. Check the sequence first: if it goes up by adding, average the ends; if it goes up by multiplying, you need the other formula entirely.

Also called summing a sequence.

What you can put on this worksheet

The sum of an arithmetic series: Find the sum of the first 7 terms: $5, 6, 7, \dots$ → $56$
The sum of a geometric series: Find the sum of the first 4 terms: $3, 9, 27, \dots$ → $120$
Given the last term: Find the sum: $3 + 7 + 11 + \dots + 51$ → $351$
In sigma notation, or to a last term: Find the sum: $\sum_{k = 1}^{4} 3 \cdot {(- 2)}^{k - 1}$ → $- 15$

Questions about these worksheets

Yes. Every arithmetic and geometric 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.

Algebra 2 is usually taken around 10th or 11th 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 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 4: the sum of an arithmetic series, the sum of a geometric series, given the last term and in sigma notation, or to a last term. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the arithmetic formula on a geometric series. Check the sequence first: if it goes up by adding, average the ends; if it goes up by multiplying, you need the other formula entirely.

Arithmetic and geometric series worksheet for Algebra 2

Sum an arithmetic series

Sum a geometric series

Sum an arithmetic series

Sum a geometric series

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these arithmetic and geometric series worksheets free?+

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

Are these arithmetic and geometric series worksheets printable?+

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

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

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

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

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

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