Recursive sequences worksheet

A recursive rule tells you how to get from one term to the next rather than jumping straight to any term. You need the first term to start, and then you step forwards. For arithmetic and geometric sequences you can shortcut it, since the step is always the same.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Recursive Sequences Date Period Find each term. A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{5}$ A sequence has $a_{1} = 8$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{6}$ A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{5}$ A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 8$ . Find $a_{6}$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{6}$ A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{6}$ A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} - 9$ . Find $a_{6}$ A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Recursive Sequences

Date Period

Find each term.

A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{5}$
A sequence has $a_{1} = 8$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{6}$
A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{5}$
A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$
A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$
A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$
A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 8$ . Find $a_{6}$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$
A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{6}$
A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{6}$
A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} - 9$ . Find $a_{6}$
A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$
A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$
A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$
A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$
A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$
A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$



Sigma Prep · sigmaprep.io/worksheets Name Recursive SequencesAnswer keyVersion 1 Date Period Find each term. A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{5}$ $43$ A sequence has $a_{1} = 8$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{6}$ $256$ A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{5}$ $36$ A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ $112$ A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ $72$ A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ $648$ A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ $567$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 8$ . Find $a_{6}$ $47$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ $42$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ $34$ A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $189$ A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{6}$ $52$ A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{6}$ $2187$ A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} - 9$ . Find $a_{6}$ $- 36$ A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $243$ A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ $44$ A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $216$ A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ $35$ A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ $56$ A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ $144$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Recursive SequencesAnswer keyVersion 1

Date Period

Find each term.

A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{5}$ $43$
A sequence has $a_{1} = 8$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{6}$ $256$
A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{5}$ $36$
A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ $112$
A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ $72$
A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ $648$
A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{5}$ $567$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 8$ . Find $a_{6}$ $47$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ $42$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ $34$
A sequence has $a_{1} = 7$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $189$
A sequence has $a_{1} = 7$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{6}$ $52$
A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{6}$ $2187$
A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} - 9$ . Find $a_{6}$ $- 36$
A sequence has $a_{1} = 9$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $243$
A sequence has $a_{1} = 9$ and $a_{n} = a_{n - 1} + 7$ . Find $a_{6}$ $44$
A sequence has $a_{1} = 8$ and $a_{n} = 3 a_{n - 1}$ . Find $a_{4}$ $216$
A sequence has $a_{1} = 8$ and $a_{n} = a_{n - 1} + 9$ . Find $a_{4}$ $35$
A sequence has $a_{1} = 7$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{4}$ $56$
A sequence has $a_{1} = 9$ and $a_{n} = 2 a_{n - 1}$ . Find $a_{5}$ $144$

How to do these

A sequence has $a_{1} = 3$ and $a_{n} = a_{n - 1} + 4$ . Find $a_{5}$

From the 1st term to the 5th is four steps.
Four steps of plus 4 is plus 16.

The answer is $19$ .

Where students go wrong

Taking as many steps as the term number. Getting to the 5th term from the 1st is four steps, not five.

Also called recursive rule, recursive formula or term from the previous term.

Questions about these worksheets

Yes. Every recursive 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.

Algebra 2 is usually taken around 10th or 11th 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 recursive 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.

Taking as many steps as the term number. Getting to the 5th term from the 1st is four steps, not five.

Recursive sequences worksheet

Select your difficulty

Recursive Sequences

Recursive SequencesAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these recursive sequences worksheets free?+

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

Are these recursive sequences worksheets printable?+

What grade are these recursive sequences worksheets for?+

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

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

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

What do students get wrong with recursive sequences?+