Precalculus geometric series worksheet

In Precalculus geometric series are mostly written in sigma notation, and the ratio is often negative or a fraction. Read the first term, the ratio and the number of terms from the notation, then use the sum formula. It sets up infinite series, where the ratio has to be between -1 and 1.

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

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Geometric Series Date Period Find each sum. Find the sum of the first 9 terms: $5, 10, 20, \dots$ $\sum_{k = 1}^{8} 4 {(3)}^{k - 1}$ Find the sum of the first 5 terms: $- 5, - 10, - 20, \dots$ $\sum_{k = 1}^{5} - 2 {(- 2)}^{k - 1}$ Find the sum of the first 5 terms: $8, - 16, 32, \dots$ Find the sum: $- 2 - 4 - 8 + \dots - 128$ Find the sum of the first 9 terms: $- 6, 12, - 24, \dots$ Find the sum: $4 + 12 + 36 + \dots + 324$ Find the sum of the first 9 terms: $8, 24, 72, \dots$ Find the sum: $4 - 8 + 16 + \dots + 64$ Find the sum of the first 6 terms: $5, - 10, 20, \dots$ $\sum_{k = 1}^{5} {(3)}^{k - 1}$ Find the sum of the first 6 terms: $- 5, - 10, - 20, \dots$ $\sum_{k = 1}^{7} - 5 {(2)}^{k - 1}$ Find the sum of the first 7 terms: $- 7, 14, - 28, \dots$ $\sum_{k = 1}^{8} {(- 2)}^{k - 1}$ Find the sum of the first 8 terms: $- 5, - 15, - 45, \dots$ Find the sum: $- 3 + 6 - 12 + \dots + 24$ Find the sum of the first 8 terms: $5, 10, 20, \dots$ Find the sum: $2 - 4 + 8 + \dots - 256$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric Series

Date Period

Find each sum.

Find the sum of the first 9 terms: $5, 10, 20, \dots$
$\sum_{k = 1}^{8} 4 {(3)}^{k - 1}$
Find the sum of the first 5 terms: $- 5, - 10, - 20, \dots$
$\sum_{k = 1}^{5} - 2 {(- 2)}^{k - 1}$
Find the sum of the first 5 terms: $8, - 16, 32, \dots$
Find the sum: $- 2 - 4 - 8 + \dots - 128$
Find the sum of the first 9 terms: $- 6, 12, - 24, \dots$
Find the sum: $4 + 12 + 36 + \dots + 324$
Find the sum of the first 9 terms: $8, 24, 72, \dots$
Find the sum: $4 - 8 + 16 + \dots + 64$
Find the sum of the first 6 terms: $5, - 10, 20, \dots$
$\sum_{k = 1}^{5} {(3)}^{k - 1}$
Find the sum of the first 6 terms: $- 5, - 10, - 20, \dots$
$\sum_{k = 1}^{7} - 5 {(2)}^{k - 1}$
Find the sum of the first 7 terms: $- 7, 14, - 28, \dots$
$\sum_{k = 1}^{8} {(- 2)}^{k - 1}$
Find the sum of the first 8 terms: $- 5, - 15, - 45, \dots$
Find the sum: $- 3 + 6 - 12 + \dots + 24$
Find the sum of the first 8 terms: $5, 10, 20, \dots$
Find the sum: $2 - 4 + 8 + \dots - 256$



Sigma Prep · sigmaprep.io/worksheets Name Geometric SeriesAnswer keyVersion 1 Date Period Find each sum. Find the sum of the first 9 terms: $5, 10, 20, \dots$ $2555$ $\sum_{k = 1}^{8} 4 {(3)}^{k - 1}$ $13120$ Find the sum of the first 5 terms: $- 5, - 10, - 20, \dots$ $- 155$ $\sum_{k = 1}^{5} - 2 {(- 2)}^{k - 1}$ $- 22$ Find the sum of the first 5 terms: $8, - 16, 32, \dots$ $88$ Find the sum: $- 2 - 4 - 8 + \dots - 128$ $- 254$ Find the sum of the first 9 terms: $- 6, 12, - 24, \dots$ $- 1026$ Find the sum: $4 + 12 + 36 + \dots + 324$ $484$ Find the sum of the first 9 terms: $8, 24, 72, \dots$ $78728$ Find the sum: $4 - 8 + 16 + \dots + 64$ $44$ Find the sum of the first 6 terms: $5, - 10, 20, \dots$ $- 105$ $\sum_{k = 1}^{5} {(3)}^{k - 1}$ $121$ Find the sum of the first 6 terms: $- 5, - 10, - 20, \dots$ $- 315$ $\sum_{k = 1}^{7} - 5 {(2)}^{k - 1}$ $- 635$ Find the sum of the first 7 terms: $- 7, 14, - 28, \dots$ $- 301$ $\sum_{k = 1}^{8} {(- 2)}^{k - 1}$ $- 85$ Find the sum of the first 8 terms: $- 5, - 15, - 45, \dots$ $- 16400$ Find the sum: $- 3 + 6 - 12 + \dots + 24$ $15$ Find the sum of the first 8 terms: $5, 10, 20, \dots$ $1275$ Find the sum: $2 - 4 + 8 + \dots - 256$ $- 170$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric SeriesAnswer keyVersion 1

Date Period

Find each sum.

Find the sum of the first 9 terms: $5, 10, 20, \dots$ $2555$
$\sum_{k = 1}^{8} 4 {(3)}^{k - 1}$ $13120$
Find the sum of the first 5 terms: $- 5, - 10, - 20, \dots$ $- 155$
$\sum_{k = 1}^{5} - 2 {(- 2)}^{k - 1}$ $- 22$
Find the sum of the first 5 terms: $8, - 16, 32, \dots$ $88$
Find the sum: $- 2 - 4 - 8 + \dots - 128$ $- 254$
Find the sum of the first 9 terms: $- 6, 12, - 24, \dots$ $- 1026$
Find the sum: $4 + 12 + 36 + \dots + 324$ $484$
Find the sum of the first 9 terms: $8, 24, 72, \dots$ $78728$
Find the sum: $4 - 8 + 16 + \dots + 64$ $44$
Find the sum of the first 6 terms: $5, - 10, 20, \dots$ $- 105$
$\sum_{k = 1}^{5} {(3)}^{k - 1}$ $121$
Find the sum of the first 6 terms: $- 5, - 10, - 20, \dots$ $- 315$
$\sum_{k = 1}^{7} - 5 {(2)}^{k - 1}$ $- 635$
Find the sum of the first 7 terms: $- 7, 14, - 28, \dots$ $- 301$
$\sum_{k = 1}^{8} {(- 2)}^{k - 1}$ $- 85$
Find the sum of the first 8 terms: $- 5, - 15, - 45, \dots$ $- 16400$
Find the sum: $- 3 + 6 - 12 + \dots + 24$ $15$
Find the sum of the first 8 terms: $5, 10, 20, \dots$ $1275$
Find the sum: $2 - 4 + 8 + \dots - 256$ $- 170$

How to do these

$\sum_{k = 1}^{6} 5 {(- 2)}^{k - 1}$

First term 5, ratio -2, and 6 terms.
S = 5(1 - (-2)⁶)/(1 - (-2)) = 5(1 - 64)/3.
That is 5 × (-63)/3.

The answer is $- 105$ .

Where students go wrong

Dropping the parentheses on a negative ratio. (-2)⁶ is 64, but -2⁶ is -64, and that changes the sum.

Also called sum of a geometric sequence or partial sums.

What you can put on this worksheet

The sum of a geometric series: Find the sum of the first 4 terms: $3, 9, 27, \dots$ → $120$
In sigma notation, or to a last term: $\sum_{k = 1}^{4} 3 {(- 2)}^{k - 1}$ → $- 15$
Finding the number of terms: Find $n$ : $a_{1} = 4, r = - 2, S_{n} = - 20$ → $n = 4$

Questions about these worksheets

Yes. Every 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.

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 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 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: the sum of a geometric series, in sigma notation, or to a last term and finding the number of terms. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the arithmetic formula. A geometric series has no constant difference to average, so averaging the ends gives a number that has nothing to do with the sum.

Precalculus geometric series worksheet

Select your difficulty

Geometric Series

Geometric SeriesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these geometric series worksheets free?+

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

Are these geometric series worksheets printable?+

What grade are these geometric series worksheets for?+

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

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

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