Find the first four terms and a_7: a_n = 3.3 × 2^n - 1

3.3, 6.6, 13.2, 26.4 a_7 = 211.2

Geometric sequences worksheet for Precalculus

Precalculus writes geometric sequences as exponential functions of n, in the form a_n = a₁·r^(n - 1). The questions give two terms far apart, a negative or fraction ratio, or a value and ask which term it is, so the exponent has to be worked out rather than counted.

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

Select your difficulty

Pick more than one for a sheet that mixes them.

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



Sigma Prep · sigmaprep.io/worksheets Name Geometric Sequences Date Period Answer each question. Find a term of a geometric sequence What is the 7th term of the geometric sequence $4, 8, 16, 32, \dots$ ? Find the 5th term: $48, 24, 12, 6, \dots$ The sequence $- 3, - 9, - 27, - 81, \dots$ is geometric. Find $a_{6}$ . The sequence $64, 32, 16, 8, \dots$ is geometric. Find $a_{7}$ . Find the 7th term: $- 3, - 6, - 12, - 24, \dots$ What is the 5th term of the geometric sequence $- 4, - 12, - 36, - 108, \dots$ ? Find the 7th term: $128, 64, 32, 16, \dots$ Write $a_n$ from the first term and ratio, or from the first terms Write the explicit formula: $- 9,$ $- 27,$ $- 81,$ $- 243,$ $\dots$ A geometric sequence has $a_{1} = - 2$ and common ratio $r = 4$ . Write its explicit formula. Write $a_{n}$ for the geometric sequence whose first term is $4$ and whose ratio is $5$ . Find a formula for the $n$ th term of the geometric sequence $- 5, - 10, - 20, - 40, \dots$ Give the rule for $a_{n}$ , the $n$ th term of the geometric sequence $1, 4, 16, 64, \dots$ The geometric sequence $3, 6, 12, 24, \dots$ continues forever. Write $a_{n}$ in terms of $n$ . The geometric sequence $- 2,$ $- 10,$ $- 50,$ $- 250,$ $\dots$ continues forever. Write $a_{n}$ in terms of $n$ . Write $a_n$ from two terms of a geometric sequence In a geometric sequence $a_{1} = 1$ and $a_{2} = 2$ . Find $a_{n}$ In a geometric sequence $a_{3} = - 9$ and $a_{4} = 27$ . Find $a_{n}$ In a geometric sequence $a_{3} = - 8$ and $a_{4} = - 16$ . Find $a_{n}$ In a geometric sequence $a_{2} = 6$ and $a_{3} = - 18$ . Find $a_{n}$ In a geometric sequence $a_{2} = - 6$ and $a_{3} = - 18$ . Find $a_{n}$ In a geometric sequence $a_{3} = 54$ and $a_{4} = 162$ . Find $a_{n}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric Sequences

Date Period

Answer each question.

Find a term of a geometric sequence
What is the 7th term of the geometric sequence $4, 8, 16, 32, \dots$ ?
Find the 5th term: $48, 24, 12, 6, \dots$
The sequence $- 3, - 9, - 27, - 81, \dots$ is geometric. Find $a_{6}$ .
The sequence $64, 32, 16, 8, \dots$ is geometric. Find $a_{7}$ .
Find the 7th term: $- 3, - 6, - 12, - 24, \dots$
What is the 5th term of the geometric sequence $- 4, - 12, - 36, - 108, \dots$ ?
Find the 7th term: $128, 64, 32, 16, \dots$

Write $a_n$ from the first term and ratio, or from the first terms
Write the explicit formula: $- 9,$ $- 27,$ $- 81,$ $- 243,$ $\dots$
A geometric sequence has $a_{1} = - 2$ and common ratio $r = 4$ . Write its explicit formula.
Write $a_{n}$ for the geometric sequence whose first term is $4$ and whose ratio is $5$ .
Find a formula for the $n$ th term of the geometric sequence $- 5, - 10, - 20, - 40, \dots$
Give the rule for $a_{n}$ , the $n$ th term of the geometric sequence $1, 4, 16, 64, \dots$
The geometric sequence $3, 6, 12, 24, \dots$ continues forever. Write $a_{n}$ in terms of $n$ .
The geometric sequence $- 2,$ $- 10,$ $- 50,$ $- 250,$ $\dots$ continues forever. Write $a_{n}$ in terms of $n$ .

Write $a_n$ from two terms of a geometric sequence
In a geometric sequence $a_{1} = 1$ and $a_{2} = 2$ . Find $a_{n}$
In a geometric sequence $a_{3} = - 9$ and $a_{4} = 27$ . Find $a_{n}$
In a geometric sequence $a_{3} = - 8$ and $a_{4} = - 16$ . Find $a_{n}$
In a geometric sequence $a_{2} = 6$ and $a_{3} = - 18$ . Find $a_{n}$
In a geometric sequence $a_{2} = - 6$ and $a_{3} = - 18$ . Find $a_{n}$
In a geometric sequence $a_{3} = 54$ and $a_{4} = 162$ . Find $a_{n}$



Sigma Prep · sigmaprep.io/worksheets Name Geometric SequencesAnswer keyVersion 2 Date Period Answer each question. Find a term of a geometric sequence What is the 7th term of the geometric sequence $4, 8, 16, 32, \dots$ ? $256$ Find the 5th term: $48, 24, 12, 6, \dots$ $3$ The sequence $- 3, - 9, - 27, - 81, \dots$ is geometric. Find $a_{6}$ . $- 729$ The sequence $64, 32, 16, 8, \dots$ is geometric. Find $a_{7}$ . $1$ Find the 7th term: $- 3, - 6, - 12, - 24, \dots$ $- 192$ What is the 5th term of the geometric sequence $- 4, - 12, - 36, - 108, \dots$ ? $- 324$ Find the 7th term: $128, 64, 32, 16, \dots$ $2$ Write $a_n$ from the first term and ratio, or from the first terms Write the explicit formula: $- 9,$ $- 27,$ $- 81,$ $- 243,$ $\dots$ $a_{n} = - 9 \cdot 3^{n - 1}$ A geometric sequence has $a_{1} = - 2$ and common ratio $r = 4$ . Write its explicit formula. $a_{n} = - 2 \cdot 4^{n - 1}$ Write $a_{n}$ for the geometric sequence whose first term is $4$ and whose ratio is $5$ . $a_{n} = 4 \cdot 5^{n - 1}$ Find a formula for the $n$ th term of the geometric sequence $- 5, - 10, - 20, - 40, \dots$ $a_{n} = - 5 \cdot 2^{n - 1}$ Give the rule for $a_{n}$ , the $n$ th term of the geometric sequence $1, 4, 16, 64, \dots$ $a_{n} = 4^{n - 1}$ The geometric sequence $3, 6, 12, 24, \dots$ continues forever. Write $a_{n}$ in terms of $n$ . $a_{n} = 3 \cdot 2^{n - 1}$ The geometric sequence $- 2,$ $- 10,$ $- 50,$ $- 250,$ $\dots$ continues forever. Write $a_{n}$ in terms of $n$ . $a_{n} = - 2 \cdot 5^{n - 1}$ Write $a_n$ from two terms of a geometric sequence In a geometric sequence $a_{1} = 1$ and $a_{2} = 2$ . Find $a_{n}$ $a_{n} = 2^{n - 1}$ In a geometric sequence $a_{3} = - 9$ and $a_{4} = 27$ . Find $a_{n}$ $a_{n} = - {(- 3)}^{n - 1}$ In a geometric sequence $a_{3} = - 8$ and $a_{4} = - 16$ . Find $a_{n}$ $a_{n} = - 2 \cdot 2^{n - 1}$ In a geometric sequence $a_{2} = 6$ and $a_{3} = - 18$ . Find $a_{n}$ $a_{n} = - 2 \cdot {(- 3)}^{n - 1}$ In a geometric sequence $a_{2} = - 6$ and $a_{3} = - 18$ . Find $a_{n}$ $a_{n} = - 2 \cdot 3^{n - 1}$ In a geometric sequence $a_{3} = 54$ and $a_{4} = 162$ . Find $a_{n}$ $a_{n} = 6 \cdot 3^{n - 1}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric SequencesAnswer keyVersion 2

Date Period

Answer each question.

Find a term of a geometric sequence
What is the 7th term of the geometric sequence $4, 8, 16, 32, \dots$ ? $256$
Find the 5th term: $48, 24, 12, 6, \dots$ $3$
The sequence $- 3, - 9, - 27, - 81, \dots$ is geometric. Find $a_{6}$ . $- 729$
The sequence $64, 32, 16, 8, \dots$ is geometric. Find $a_{7}$ . $1$
Find the 7th term: $- 3, - 6, - 12, - 24, \dots$ $- 192$
What is the 5th term of the geometric sequence $- 4, - 12, - 36, - 108, \dots$ ? $- 324$
Find the 7th term: $128, 64, 32, 16, \dots$ $2$

Write $a_n$ from the first term and ratio, or from the first terms
Write the explicit formula: $- 9,$ $- 27,$ $- 81,$ $- 243,$ $\dots$ $a_{n} = - 9 \cdot 3^{n - 1}$
A geometric sequence has $a_{1} = - 2$ and common ratio $r = 4$ . Write its explicit formula. $a_{n} = - 2 \cdot 4^{n - 1}$
Write $a_{n}$ for the geometric sequence whose first term is $4$ and whose ratio is $5$ . $a_{n} = 4 \cdot 5^{n - 1}$
Find a formula for the $n$ th term of the geometric sequence $- 5, - 10, - 20, - 40, \dots$ $a_{n} = - 5 \cdot 2^{n - 1}$
Give the rule for $a_{n}$ , the $n$ th term of the geometric sequence $1, 4, 16, 64, \dots$ $a_{n} = 4^{n - 1}$
The geometric sequence $3, 6, 12, 24, \dots$ continues forever. Write $a_{n}$ in terms of $n$ . $a_{n} = 3 \cdot 2^{n - 1}$
The geometric sequence $- 2,$ $- 10,$ $- 50,$ $- 250,$ $\dots$ continues forever. Write $a_{n}$ in terms of $n$ . $a_{n} = - 2 \cdot 5^{n - 1}$

Write $a_n$ from two terms of a geometric sequence
In a geometric sequence $a_{1} = 1$ and $a_{2} = 2$ . Find $a_{n}$ $a_{n} = 2^{n - 1}$
In a geometric sequence $a_{3} = - 9$ and $a_{4} = 27$ . Find $a_{n}$ $a_{n} = - {(- 3)}^{n - 1}$
In a geometric sequence $a_{3} = - 8$ and $a_{4} = - 16$ . Find $a_{n}$ $a_{n} = - 2 \cdot 2^{n - 1}$
In a geometric sequence $a_{2} = 6$ and $a_{3} = - 18$ . Find $a_{n}$ $a_{n} = - 2 \cdot {(- 3)}^{n - 1}$
In a geometric sequence $a_{2} = - 6$ and $a_{3} = - 18$ . Find $a_{n}$ $a_{n} = - 2 \cdot 3^{n - 1}$
In a geometric sequence $a_{3} = 54$ and $a_{4} = 162$ . Find $a_{n}$ $a_{n} = 6 \cdot 3^{n - 1}$

How to do these

$a_{2} = 6$ and $a_{5} = - 48$ . Write the explicit formula for $a_{n}$

a₅ is three multiplications past a₂, so r³ = -48 ÷ 6 = -8 and r = -2.
Step back once: a₁ = 6 ÷ (-2) = -3.

The answer is $a_{n} = - 3 {(- 2)}^{n - 1}$ .

Where students go wrong

Taking the plain quotient of the two terms as the ratio. a₅ is three steps past a₂, so -48 ÷ 6 = -8 is r cubed, and r itself is -2.

Also called common ratio or nth term of a geometric sequence.

What you can put on this worksheet

A given term of a geometric sequence: Find the 6th term: $64, 32, 16, 8, \dots$ → $2$
The explicit formula: Write $a_{n}$ for the geometric sequence whose first term is $- 1$ and whose ratio is $4$ . → $a_{n} = - 4^{n - 1}$
From two terms: In a geometric sequence $a_{1} = 4$ and $a_{2} = - 8$ . Find $a_{n}$ → $a_{n} = 4 \cdot {(- 2)}^{n - 1}$
Terms from a formula, both formulas, back from a later term: Find the first four terms and $a_{7}$ : $a_{n} = 3.3 \cdot 2^{n - 1}$ → $3.3,$ $6.6,$ $13.2,$ $26.4 a_{7} = 211.2$

Questions about these worksheets

Yes. Every 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 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 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 4: a given term of a geometric sequence, the explicit formula, from two terms and terms from a formula, both formulas, back from a later term. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the term number as the exponent. The sixth term uses 2 to the fifth, not the sixth, for the same reason arithmetic sequences take one step fewer than you expect.

Geometric sequences worksheet for Precalculus

Select your difficulty

Find a term of a geometric sequence

Write ana_nan​ from the first term and ratio, or from the first terms

Write ana_nan​ from two terms of a geometric sequence

Find a term of a geometric sequence

Write ana_nan​ from the first term and ratio, or from the first terms

Write ana_nan​ from two terms of a geometric sequence

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these geometric sequences worksheets free?+

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

Are these geometric sequences worksheets printable?+

What grade are these geometric sequences worksheets for?+

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

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

Can I choose how hard the geometric sequences questions are?+

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

What do students get wrong with geometric sequences?+

Write $a_n$ from the first term and ratio, or from the first terms

Write $a_n$ from two terms of a geometric sequence

Write $a_n$ from the first term and ratio, or from the first terms

Write $a_n$ from two terms of a geometric sequence