Comparing arithmetic and geometric sequences worksheet for Precalculus

Precalculus gives sequences with negative terms, negative ratios and patterns that only look regular at first. The test is unchanged: a constant difference means arithmetic, a constant ratio means geometric, and if neither holds all the way along, the answer is neither.

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 or Geometric Date Period Answer each question. Decide if it is arithmetic or geometric, and find the common difference or ratio Arithmetic or geometric? Give the common difference or ratio: $- 2, 6, 14, 22, \dots$ Arithmetic or geometric? Give the common difference or ratio: $12, 24, 48, 96, \dots$ Arithmetic or geometric? Give the common difference or ratio: $- 10,$ $- 22,$ $- 34,$ $- 46,$ $\dots$ Arithmetic or geometric? Give the common difference or ratio: $- 4, - 2, 0, 2, \dots$ Arithmetic or geometric? Give the common difference or ratio: $12, - 3, - 18, - 33, \dots$ Arithmetic or geometric? Give the common difference or ratio: $10, - 1, - 12, - 23, \dots$ Arithmetic or geometric? Give the common difference or ratio: $4, 8, 12, 16, \dots$ Arithmetic or geometric? Give the common difference or ratio: $13, 0, - 13, - 26, \dots$ Arithmetic or geometric? Give the common difference or ratio: $- 8,$ $- 32,$ $- 128,$ $- 512,$ $\dots$ Arithmetic or geometric? Give the common difference or ratio: $3, 9, 27, 81, \dots$ Decide if it is arithmetic, geometric or neither Arithmetic, geometric, or neither? $- 2, 6, - 18, 54, \dots$ Arithmetic, geometric, or neither? $2, 5, 10, 17, \dots$ Arithmetic, geometric, or neither? $- 7, - 8, - 9, - 10, \dots$ Arithmetic, geometric, or neither? $9, 0, - 9, - 18, \dots$ Arithmetic, geometric, or neither? $- 8, - 1, 6, 13, \dots$ Arithmetic, geometric, or neither? $- 5, 0, 5, 10, \dots$ Arithmetic, geometric, or neither? $6, 12, 18, 24, \dots$ Arithmetic, geometric, or neither? $- 8, - 11, - 14, - 17, \dots$ Arithmetic, geometric, or neither? $5, 9, 17, 33, \dots$ Arithmetic, geometric, or neither? $5, 10, 17, 26, \dots$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic or Geometric

Date Period

Answer each question.

Decide if it is arithmetic or geometric, and find the common difference or ratio
Arithmetic or geometric? Give the common difference or ratio: $- 2, 6, 14, 22, \dots$
Arithmetic or geometric? Give the common difference or ratio: $12, 24, 48, 96, \dots$
Arithmetic or geometric? Give the common difference or ratio: $- 10,$ $- 22,$ $- 34,$ $- 46,$ $\dots$
Arithmetic or geometric? Give the common difference or ratio: $- 4, - 2, 0, 2, \dots$
Arithmetic or geometric? Give the common difference or ratio: $12, - 3, - 18, - 33, \dots$
Arithmetic or geometric? Give the common difference or ratio: $10, - 1, - 12, - 23, \dots$
Arithmetic or geometric? Give the common difference or ratio: $4, 8, 12, 16, \dots$
Arithmetic or geometric? Give the common difference or ratio: $13, 0, - 13, - 26, \dots$
Arithmetic or geometric? Give the common difference or ratio: $- 8,$ $- 32,$ $- 128,$ $- 512,$ $\dots$
Arithmetic or geometric? Give the common difference or ratio: $3, 9, 27, 81, \dots$

Decide if it is arithmetic, geometric or neither
Arithmetic, geometric, or neither? $- 2, 6, - 18, 54, \dots$
Arithmetic, geometric, or neither? $2, 5, 10, 17, \dots$
Arithmetic, geometric, or neither? $- 7, - 8, - 9, - 10, \dots$
Arithmetic, geometric, or neither? $9, 0, - 9, - 18, \dots$
Arithmetic, geometric, or neither? $- 8, - 1, 6, 13, \dots$
Arithmetic, geometric, or neither? $- 5, 0, 5, 10, \dots$
Arithmetic, geometric, or neither? $6, 12, 18, 24, \dots$
Arithmetic, geometric, or neither? $- 8, - 11, - 14, - 17, \dots$
Arithmetic, geometric, or neither? $5, 9, 17, 33, \dots$
Arithmetic, geometric, or neither? $5, 10, 17, 26, \dots$



Sigma Prep · sigmaprep.io/worksheets Name Arithmetic or GeometricAnswer keyVersion 2 Date Period Answer each question. Decide if it is arithmetic or geometric, and find the common difference or ratio Arithmetic or geometric? Give the common difference or ratio: $- 2, 6, 14, 22, \dots$ Arithmetic, $d = 8$ Arithmetic or geometric? Give the common difference or ratio: $12, 24, 48, 96, \dots$ Geometric, $r = 2$ Arithmetic or geometric? Give the common difference or ratio: $- 10,$ $- 22,$ $- 34,$ $- 46,$ $\dots$ Arithmetic, $d = - 12$ Arithmetic or geometric? Give the common difference or ratio: $- 4, - 2, 0, 2, \dots$ Arithmetic, $d = 2$ Arithmetic or geometric? Give the common difference or ratio: $12, - 3, - 18, - 33, \dots$ Arithmetic, $d = - 15$ Arithmetic or geometric? Give the common difference or ratio: $10, - 1, - 12, - 23, \dots$ Arithmetic, $d = - 11$ Arithmetic or geometric? Give the common difference or ratio: $4, 8, 12, 16, \dots$ Arithmetic, $d = 4$ Arithmetic or geometric? Give the common difference or ratio: $13, 0, - 13, - 26, \dots$ Arithmetic, $d = - 13$ Arithmetic or geometric? Give the common difference or ratio: $- 8,$ $- 32,$ $- 128,$ $- 512,$ $\dots$ Geometric, $r = 4$ Arithmetic or geometric? Give the common difference or ratio: $3, 9, 27, 81, \dots$ Geometric, $r = 3$ Decide if it is arithmetic, geometric or neither Arithmetic, geometric, or neither? $- 2, 6, - 18, 54, \dots$ Geometric, $r = - 3$ Arithmetic, geometric, or neither? $2, 5, 10, 17, \dots$ Neither Arithmetic, geometric, or neither? $- 7, - 8, - 9, - 10, \dots$ Arithmetic, $d = - 1$ Arithmetic, geometric, or neither? $9, 0, - 9, - 18, \dots$ Arithmetic, $d = - 9$ Arithmetic, geometric, or neither? $- 8, - 1, 6, 13, \dots$ Arithmetic, $d = 7$ Arithmetic, geometric, or neither? $- 5, 0, 5, 10, \dots$ Arithmetic, $d = 5$ Arithmetic, geometric, or neither? $6, 12, 18, 24, \dots$ Arithmetic, $d = 6$ Arithmetic, geometric, or neither? $- 8, - 11, - 14, - 17, \dots$ Arithmetic, $d = - 3$ Arithmetic, geometric, or neither? $5, 9, 17, 33, \dots$ Neither Arithmetic, geometric, or neither? $5, 10, 17, 26, \dots$ Neither Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Arithmetic or GeometricAnswer keyVersion 2

Date Period

Answer each question.

Decide if it is arithmetic or geometric, and find the common difference or ratio
Arithmetic or geometric? Give the common difference or ratio: $- 2, 6, 14, 22, \dots$ Arithmetic, $d = 8$
Arithmetic or geometric? Give the common difference or ratio: $12, 24, 48, 96, \dots$ Geometric, $r = 2$
Arithmetic or geometric? Give the common difference or ratio: $- 10,$ $- 22,$ $- 34,$ $- 46,$ $\dots$ Arithmetic, $d = - 12$
Arithmetic or geometric? Give the common difference or ratio: $- 4, - 2, 0, 2, \dots$ Arithmetic, $d = 2$
Arithmetic or geometric? Give the common difference or ratio: $12, - 3, - 18, - 33, \dots$ Arithmetic, $d = - 15$
Arithmetic or geometric? Give the common difference or ratio: $10, - 1, - 12, - 23, \dots$ Arithmetic, $d = - 11$
Arithmetic or geometric? Give the common difference or ratio: $4, 8, 12, 16, \dots$ Arithmetic, $d = 4$
Arithmetic or geometric? Give the common difference or ratio: $13, 0, - 13, - 26, \dots$ Arithmetic, $d = - 13$
Arithmetic or geometric? Give the common difference or ratio: $- 8,$ $- 32,$ $- 128,$ $- 512,$ $\dots$ Geometric, $r = 4$
Arithmetic or geometric? Give the common difference or ratio: $3, 9, 27, 81, \dots$ Geometric, $r = 3$

Decide if it is arithmetic, geometric or neither
Arithmetic, geometric, or neither? $- 2, 6, - 18, 54, \dots$ Geometric, $r = - 3$
Arithmetic, geometric, or neither? $2, 5, 10, 17, \dots$ Neither
Arithmetic, geometric, or neither? $- 7, - 8, - 9, - 10, \dots$ Arithmetic, $d = - 1$
Arithmetic, geometric, or neither? $9, 0, - 9, - 18, \dots$ Arithmetic, $d = - 9$
Arithmetic, geometric, or neither? $- 8, - 1, 6, 13, \dots$ Arithmetic, $d = 7$
Arithmetic, geometric, or neither? $- 5, 0, 5, 10, \dots$ Arithmetic, $d = 5$
Arithmetic, geometric, or neither? $6, 12, 18, 24, \dots$ Arithmetic, $d = 6$
Arithmetic, geometric, or neither? $- 8, - 11, - 14, - 17, \dots$ Arithmetic, $d = - 3$
Arithmetic, geometric, or neither? $5, 9, 17, 33, \dots$ Neither
Arithmetic, geometric, or neither? $5, 10, 17, 26, \dots$ Neither

How to do these

Arithmetic, geometric, or neither? $48, - 24, 12, - 6, \dots$

The differences are -72, 36, -18, so it is not arithmetic.
Each term is -1/2 times the one before, so the ratio is constant.

The answer is Geometric, $r = - \frac{1}{2}$ .

Where students go wrong

Checking only the first pair of terms. 1, 4, 9, 16 starts with a difference of 3, but the next differences are 5 and 7, and the ratios change too, so it is neither.

Also called arithmetic means.

What you can put on this worksheet

Arithmetic or geometric, and the step: Arithmetic or geometric? Give the common difference or ratio: $5, 1, - 3, - 7, \dots$ → Arithmetic, $d = - 4$
Arithmetic, geometric, or neither: Arithmetic, geometric, or neither? $4, 8, 16, 32, \dots$ → Geometric, $r = 2$
Lists with fractions, explicit and recursive formulas: Arithmetic, geometric or neither? $a_{n} = \frac{n}{3^{n}}$ → Neither

Questions about these worksheets

Yes. Every comparing arithmetic and geometric sequences 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 comparing arithmetic and geometric sequences 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: arithmetic or geometric, and the step, arithmetic, geometric, or neither and lists with fractions, explicit and recursive formulas. Tick as many as you want and set how many of each, or let it spread them evenly.

Checking only the first pair. 2, 4, 6, 12 starts like a geometric sequence and is neither, so the step has to hold all the way along before you name it.

Comparing arithmetic and geometric sequences worksheet for Precalculus

Decide if it is arithmetic or geometric, and find the common difference or ratio

Decide if it is arithmetic, geometric or neither

Decide if it is arithmetic or geometric, and find the common difference or ratio

Decide if it is arithmetic, geometric or neither

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these comparing arithmetic and geometric sequences worksheets free?+

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

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

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

What do students get wrong with comparing arithmetic and geometric sequences?+