Precalculus sequences and series worksheet

Two basics that everything else in the unit sits on: getting a term out of a formula, and reading sigma notation as an instruction to add.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Sequences and Series Date Period Answer each question. Given $a_{n} = 11 n + 25$ , find $a_{10}$ $\sum_{k = 2}^{7} (11 k - 20)$ Given $a_{n} = - 12 n^{2} - 20$ , find $a_{12}$ $\sum_{k = 1}^{7} (10 k - 13)$ Given $a_{n} = 12 n - 22$ , find $a_{18}$ $\sum_{k = 6}^{9} (- 11 k - 19)$ Given $a_{n} = - 12 n^{2} - 18$ , find $a_{18}$ $\sum_{k = 1}^{8} (9 k - 13)$ Given $a_{n} = - 15 n^{2} + 20$ , find $a_{17}$ $\sum_{k = 1}^{9} (12 k + 20)$ Given $a_{n} = - 11 n + 18$ , find $a_{14}$ $\sum_{k = 7}^{9} (11 k - 18)$ Given $a_{n} = - 12 n^{2} - 20$ , find $a_{17}$ $\sum_{k = 2}^{9} (11 k - 19)$ Given $a_{n} = - 15 n - 17$ , find $a_{15}$ $\sum_{k = 1}^{6} (- 9 k - 13)$ Given $a_{n} = 11 n^{2} + 21$ , find $a_{19}$ $\sum_{k = 2}^{5} (- 12 k + 19)$ Given $a_{n} = 12 n^{2} + 24$ , find $a_{10}$ $\sum_{k = 2}^{5} (12 k + 14)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Sequences and Series

Date Period

Answer each question.

Given $a_{n} = 11 n + 25$ , find $a_{10}$
$\sum_{k = 2}^{7} (11 k - 20)$
Given $a_{n} = - 12 n^{2} - 20$ , find $a_{12}$
$\sum_{k = 1}^{7} (10 k - 13)$
Given $a_{n} = 12 n - 22$ , find $a_{18}$
$\sum_{k = 6}^{9} (- 11 k - 19)$
Given $a_{n} = - 12 n^{2} - 18$ , find $a_{18}$
$\sum_{k = 1}^{8} (9 k - 13)$
Given $a_{n} = - 15 n^{2} + 20$ , find $a_{17}$
$\sum_{k = 1}^{9} (12 k + 20)$
Given $a_{n} = - 11 n + 18$ , find $a_{14}$
$\sum_{k = 7}^{9} (11 k - 18)$
Given $a_{n} = - 12 n^{2} - 20$ , find $a_{17}$
$\sum_{k = 2}^{9} (11 k - 19)$
Given $a_{n} = - 15 n - 17$ , find $a_{15}$
$\sum_{k = 1}^{6} (- 9 k - 13)$
Given $a_{n} = 11 n^{2} + 21$ , find $a_{19}$
$\sum_{k = 2}^{5} (- 12 k + 19)$
Given $a_{n} = 12 n^{2} + 24$ , find $a_{10}$
$\sum_{k = 2}^{5} (12 k + 14)$



Sigma Prep · sigmaprep.io/worksheets Name Sequences and SeriesAnswer keyVersion 1 Date Period Answer each question. Given $a_{n} = 11 n + 25$ , find $a_{10}$ $135$ $\sum_{k = 2}^{7} (11 k - 20)$ $177$ Given $a_{n} = - 12 n^{2} - 20$ , find $a_{12}$ $- 1748$ $\sum_{k = 1}^{7} (10 k - 13)$ $189$ Given $a_{n} = 12 n - 22$ , find $a_{18}$ $194$ $\sum_{k = 6}^{9} (- 11 k - 19)$ $- 406$ Given $a_{n} = - 12 n^{2} - 18$ , find $a_{18}$ $- 3906$ $\sum_{k = 1}^{8} (9 k - 13)$ $220$ Given $a_{n} = - 15 n^{2} + 20$ , find $a_{17}$ $- 4315$ $\sum_{k = 1}^{9} (12 k + 20)$ $720$ Given $a_{n} = - 11 n + 18$ , find $a_{14}$ $- 136$ $\sum_{k = 7}^{9} (11 k - 18)$ $210$ Given $a_{n} = - 12 n^{2} - 20$ , find $a_{17}$ $- 3488$ $\sum_{k = 2}^{9} (11 k - 19)$ $332$ Given $a_{n} = - 15 n - 17$ , find $a_{15}$ $- 242$ $\sum_{k = 1}^{6} (- 9 k - 13)$ $- 267$ Given $a_{n} = 11 n^{2} + 21$ , find $a_{19}$ $3992$ $\sum_{k = 2}^{5} (- 12 k + 19)$ $- 92$ Given $a_{n} = 12 n^{2} + 24$ , find $a_{10}$ $1224$ $\sum_{k = 2}^{5} (12 k + 14)$ $224$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Sequences and SeriesAnswer keyVersion 1

Date Period

Answer each question.

Given $a_{n} = 11 n + 25$ , find $a_{10}$ $135$
$\sum_{k = 2}^{7} (11 k - 20)$ $177$
Given $a_{n} = - 12 n^{2} - 20$ , find $a_{12}$ $- 1748$
$\sum_{k = 1}^{7} (10 k - 13)$ $189$
Given $a_{n} = 12 n - 22$ , find $a_{18}$ $194$
$\sum_{k = 6}^{9} (- 11 k - 19)$ $- 406$
Given $a_{n} = - 12 n^{2} - 18$ , find $a_{18}$ $- 3906$
$\sum_{k = 1}^{8} (9 k - 13)$ $220$
Given $a_{n} = - 15 n^{2} + 20$ , find $a_{17}$ $- 4315$
$\sum_{k = 1}^{9} (12 k + 20)$ $720$
Given $a_{n} = - 11 n + 18$ , find $a_{14}$ $- 136$
$\sum_{k = 7}^{9} (11 k - 18)$ $210$
Given $a_{n} = - 12 n^{2} - 20$ , find $a_{17}$ $- 3488$
$\sum_{k = 2}^{9} (11 k - 19)$ $332$
Given $a_{n} = - 15 n - 17$ , find $a_{15}$ $- 242$
$\sum_{k = 1}^{6} (- 9 k - 13)$ $- 267$
Given $a_{n} = 11 n^{2} + 21$ , find $a_{19}$ $3992$
$\sum_{k = 2}^{5} (- 12 k + 19)$ $- 92$
Given $a_{n} = 12 n^{2} + 24$ , find $a_{10}$ $1224$
$\sum_{k = 2}^{5} (12 k + 14)$ $224$

How to do these

Given $a_{n} = 3 n - 2$ , find $a_{7}$

Put 7 in for n.
3 times 7 is 21, minus 2.

The answer is $19$ .

Where students go wrong

Reading a_7 as the seventh thing you write rather than n = 7. They are the same here, but with a recursive formula they are not, and the habit matters later.

Also called nth term, sigma notation or summation notation.

What you can put on this worksheet

A term from an explicit formula: Given $a_{n} = 4 n$ , find $a_{5}$ → $20$
Add up a short series: $\sum_{k = 1}^{4} (3 k)$ → $30$

Questions about these worksheets

Yes. Every sequences and 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 sequences and 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 2: a term from an explicit formula and add up a short series. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading a_7 as the seventh thing you write rather than n = 7. They are the same here, but with a recursive formula they are not, and the habit matters later.

Precalculus sequences and series worksheet

Select your difficulty

Sequences and Series

Sequences and SeriesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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