Precalculus geometric mean worksheet

In Precalculus geometric means are terms of a geometric sequence: inserting them means finding the common ratio from the two ends. When an even power of the ratio is given, the ratio can be positive or negative, and both give a valid set of means.

Also taught in Algebra 2 and Geometry, each 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 Mean Date Period Answer each question. Find the geometric mean of $20$ and $2$ Insert two geometric means between $6$ and $- 48$ Find the geometric mean of $14$ and $50$ Insert two geometric means between $- 1$ and $- 64$ Find the geometric mean of $6$ and $42$ Insert two geometric means between $- 6$ and $162$ Find the geometric mean of $14$ and $12$ Insert two geometric means between $3$ and $24$ Find the geometric mean of $16$ and $3$ Insert two geometric means between $- 3$ and $- 81$ Find the geometric mean of $7$ and $27$ Insert two geometric means between $3$ and $- 192$ Find the geometric mean of $2$ and $42$ Insert two geometric means between $4$ and $108$ Find the geometric mean of $13$ and $4$ Insert two geometric means between $- 5$ and $40$ Find the geometric mean of $25$ and $46$ Insert two geometric means between $6$ and $384$ Find the geometric mean of $25$ and $47$ Insert two geometric means between $- 5$ and $320$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric Mean

Date Period

Answer each question.

Find the geometric mean of $20$ and $2$
Insert two geometric means between $6$ and $- 48$
Find the geometric mean of $14$ and $50$
Insert two geometric means between $- 1$ and $- 64$
Find the geometric mean of $6$ and $42$
Insert two geometric means between $- 6$ and $162$
Find the geometric mean of $14$ and $12$
Insert two geometric means between $3$ and $24$
Find the geometric mean of $16$ and $3$
Insert two geometric means between $- 3$ and $- 81$
Find the geometric mean of $7$ and $27$
Insert two geometric means between $3$ and $- 192$
Find the geometric mean of $2$ and $42$
Insert two geometric means between $4$ and $108$
Find the geometric mean of $13$ and $4$
Insert two geometric means between $- 5$ and $40$
Find the geometric mean of $25$ and $46$
Insert two geometric means between $6$ and $384$
Find the geometric mean of $25$ and $47$
Insert two geometric means between $- 5$ and $320$



Sigma Prep · sigmaprep.io/worksheets Name Geometric MeanAnswer keyVersion 1 Date Period Answer each question. Find the geometric mean of $20$ and $2$ $2 \sqrt{10}$ Insert two geometric means between $6$ and $- 48$ $- 12, 24$ Find the geometric mean of $14$ and $50$ $10 \sqrt{7}$ Insert two geometric means between $- 1$ and $- 64$ $- 4, - 16$ Find the geometric mean of $6$ and $42$ $6 \sqrt{7}$ Insert two geometric means between $- 6$ and $162$ $18, - 54$ Find the geometric mean of $14$ and $12$ $2 \sqrt{42}$ Insert two geometric means between $3$ and $24$ $6, 12$ Find the geometric mean of $16$ and $3$ $4 \sqrt{3}$ Insert two geometric means between $- 3$ and $- 81$ $- 9, - 27$ Find the geometric mean of $7$ and $27$ $3 \sqrt{21}$ Insert two geometric means between $3$ and $- 192$ $- 12, 48$ Find the geometric mean of $2$ and $42$ $2 \sqrt{21}$ Insert two geometric means between $4$ and $108$ $12, 36$ Find the geometric mean of $13$ and $4$ $2 \sqrt{13}$ Insert two geometric means between $- 5$ and $40$ $10, - 20$ Find the geometric mean of $25$ and $46$ $5 \sqrt{46}$ Insert two geometric means between $6$ and $384$ $24, 96$ Find the geometric mean of $25$ and $47$ $5 \sqrt{47}$ Insert two geometric means between $- 5$ and $320$ $20, - 80$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric MeanAnswer keyVersion 1

Date Period

Answer each question.

Find the geometric mean of $20$ and $2$ $2 \sqrt{10}$
Insert two geometric means between $6$ and $- 48$ $- 12, 24$
Find the geometric mean of $14$ and $50$ $10 \sqrt{7}$
Insert two geometric means between $- 1$ and $- 64$ $- 4, - 16$
Find the geometric mean of $6$ and $42$ $6 \sqrt{7}$
Insert two geometric means between $- 6$ and $162$ $18, - 54$
Find the geometric mean of $14$ and $12$ $2 \sqrt{42}$
Insert two geometric means between $3$ and $24$ $6, 12$
Find the geometric mean of $16$ and $3$ $4 \sqrt{3}$
Insert two geometric means between $- 3$ and $- 81$ $- 9, - 27$
Find the geometric mean of $7$ and $27$ $3 \sqrt{21}$
Insert two geometric means between $3$ and $- 192$ $- 12, 48$
Find the geometric mean of $2$ and $42$ $2 \sqrt{21}$
Insert two geometric means between $4$ and $108$ $12, 36$
Find the geometric mean of $13$ and $4$ $2 \sqrt{13}$
Insert two geometric means between $- 5$ and $40$ $10, - 20$
Find the geometric mean of $25$ and $46$ $5 \sqrt{46}$
Insert two geometric means between $6$ and $384$ $24, 96$
Find the geometric mean of $25$ and $47$ $5 \sqrt{47}$
Insert two geometric means between $- 5$ and $320$ $20, - 80$

How to do these

Insert three geometric means between $2$ and $162$

Four steps of the ratio take 2 to 162, so r⁴ = 81.
r = 3 or r = -3.
With 3: 6, 18, 54. With -3: -6, 18, -54.

The answer is $6, 18, 54$ or $- 6, 18, - 54$ .

Where students go wrong

Taking only the positive root. An even power hides the sign, so r⁴ = 81 allows r = -3 as well, and that gives a second set of means.

Also called geometric mean, geometric means, inserting geometric means or geometric mean of two numbers.

What you can put on this worksheet

The geometric mean of two numbers: Find the geometric mean of $6$ and $24$ → $12$
Insert geometric means between two numbers: Insert two geometric means between $3$ and $81$ → $9, 27$
The geometric mean in a right triangle: Find the altitude — a right triangle with the altitude drawn to its hypotenuse, labeled 5, 5, x → $5$
Negative ends, three means, fractions: both signs of the ratio: Find the missing terms of the geometric sequence: $625,___,___,___, 1$ → $125, 25, 5$ or $- 125, 25, - 5$

Questions about these worksheets

Yes. Every geometric mean 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 mean 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 geometric mean of two numbers, insert geometric means between two numbers, the geometric mean in a right triangle and negative ends, three means, fractions: both signs of the ratio. Tick as many as you want and set how many of each, or let it spread them evenly.

Averaging instead: the numbers halfway between 3 and 81 are arithmetic means. Geometric means multiply by the same number each step, they do not add.

Precalculus geometric mean worksheet

Select your difficulty

Geometric Mean

Geometric MeanAnswer 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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