Algebra 1 Arithmetic and Geometric Sequences Worksheet (PDF)

Algebra 1 math worksheet: Arithmetic and Geometric Sequences – Maths PDF

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This sequences practice worksheet for Algebra 1 covers arithmetic and geometric sequences (Common Core F-IF.A.3, F-BF.A.1a, F-BF.A.2, F-LE.A.2), with a free PDF to print.

Use these 20 problems to master arithmetic and geometric sequences (Common Core F-IF.A.3, F-BF.A.1a, F-BF.A.2, and F-LE.A.2). You will find common differences and ratios, write recursive and explicit rules, read sequences from graphs and patterns, and model growth in real situations. They move from quick warm-ups to multistep word problems, so slow down on the last six and check that each answer makes sense.

Algebra 1 · Common Core State Standards: F-IF.A.3, F-BF.A.1a, F-BF.A.2, F-LE.A.2

Sequences practice worksheet: exercises 1 to 10

Exercise 1 – Next terms

A pattern.

Find the next three terms of the sequence $8, 13, 18, 23$.

Exercise 2 – Arithmetic or geometric?

Decide whether $3, 6, 12, 24$ is arithmetic, geometric, or neither.

Exercise 3 – Common difference

Find the common difference of $40, 33, 26, 19$.

Exercise 4 – Common ratio

Population at the start of each decade.

A town’s population multiplies by the same factor each decade: $2500, 3000, 3600, 4320$. Find the common ratio and the population at the start of the next decade.

Exercise 5 – Explicit rule

Write an explicit rule for $7, 12, 17, 22$.

Exercise 6 – A distant term

Find the 20th term of the sequence $4, 7, 10, 13$.

Exercise 7 – Recursive rule

Write a recursive rule for $10, 6, 2, -2$.

Exercise 8 – Geometric explicit rule

Terms of a geometric sequence.

Write an explicit rule for $3, 6, 12, 24$ and find the 6th term.

Exercise 9 – Fractional ratio

Write an explicit rule for $81, 27, 9, 3$ and find the 5th term.

Exercise 10 – Which term?

Which term of $5, 10, 15, 20$ equals 95?

Exercises 11 and up

Exercise 11 – Two terms given

An arithmetic sequence has $a_{2} = 5$ and $a_{6} = 21$. Find the common difference and a rule for $a_{n}$.

Exercise 12 – Evaluate a recursive rule

A sequence is defined by $a_{1} = 2$ and $a_{n} = 3a_{n-1} – 1$. Find $a_{4}$.

Exercise 13 – Is 100 in the sequence?

Is 100 a term of $7, 12, 17, 22$?

Exercise 14 – Graph of a sequence

Four terms of a sequence.

The graph shows the first four terms of an arithmetic sequence. Write its explicit rule.

Exercise 15 – Pattern of squares

Three figures.

The figures use 5, 7, and 9 squares. Write a rule for the number of squares in Figure $n$ and find Figure 10.

Exercise 16 – Weekly savings

Maya saves $15 in week 1, $20 in week 2, $25 in week 3, and keeps adding $5 more each week. Write a rule for the amount in week $n$. Find week 12 and the week in which she saves $100.

Exercise 17 – Bouncing ball

Bounce heights in feet.

A ball’s bounce heights are 64 ft, 32 ft, 16 ft, 8 ft. Write an explicit rule and find the 5th bounce.

Exercise 18 – Bacteria growth

A lab starts with 250 bacteria, and the number doubles every hour. Let $a_{1} = 250$ be the count at hour 0. Write an explicit rule and find the count after 5 hours.

Exercise 19 – Stadium seats

Row 1 of a stadium section has 20 seats and each row has 2 more seats than the row before. Write a rule for row $n$. How many seats are in row 25? Which row has 100 seats?

Exercise 20 – Yearly raise

Liam’s job pays $40,000 in year 1 and gives a 5% raise each year. Write a rule for his pay in year $n$ and find his pay in year 4.

Exercise 21 – Two pay plans

Daily pay for two plans.

Plan A pays $2 on day 1 and $3 more each day. Plan B pays $1 on day 1 and doubles each day. Write rules for both plans and find the first day when Plan B pays more than Plan A.

Key facts behind this sequences practice worksheet

Key facts

A sequence is a function whose inputs are the positions 1, 2, 3, and so on.
Arithmetic: add d each time; aₙ = a₁ + (n – 1)d.
Geometric: multiply by r each time; aₙ = a₁ · r^(n-1).
A recursive rule gives each term from the previous term; an explicit rule gives any term directly.
Arithmetic sequences are linear; geometric sequences are exponential.

How to use this sequences practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the sequences practice worksheet as a PDF with the button below and keep it with your notes.

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