Algebra 2 Arithmetic and Geometric Sequences and Series Worksheet (PDF)

Algebra 2 math worksheet: Arithmetic and Geometric Sequences and Series – Maths PDF

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This algebra 2 sequences series worksheet for Algebra 2 covers arithmetic and geometric sequences and series (Common Core F-BF.A.2, A-SSE.B.4, F-IF.A.3), with a free PDF to print.

These 20 problems practice arithmetic and geometric sequences and series (Common Core F-BF.A.2, A-SSE.B.4 and F-IF.A.3). The first problems check listing terms and recognizing arithmetic and geometric patterns, the middle problems add explicit and recursive formulas and the sum formulas, and the last six are word problems and multi-step tasks that need savings, seating, and doubling problems.

Work in order and show every step. Write each answer in simplest form, and open the answer key only after you have tried the problem yourself.

Algebra 2 · Common Core State Standards: F-BF.A.2, A-SSE.B.4, F-IF.A.3

Algebra 2 sequences series worksheet: exercises 1 to 10

Exercise 1 – List the terms

Write the first five terms of $a_{n} = 3n – 2$.

Exercise 2 – Recursive formula

Write the first five terms of the sequence with $a_{1} = 5$ and $a_{n} = a_{n-1} + 4$.

Exercise 3 – Arithmetic or geometric?

Identify each sequence.

Decide whether each sequence in the table is arithmetic, geometric, or neither.

Exercise 4 – Explicit arithmetic formula

Write an explicit formula for $7, 11, 15, 19, …$ and find $a_{20}$.

Exercise 5 – Find a term

An arithmetic sequence has $a_{1} = -4$ and $d = 3$. Find $a_{15}$.

Exercise 6 – Find the position

Which term of $2, 5, 8, 11, …$ equals 62?

Exercise 7 – Geometric formula

Write an explicit formula for $3, 6, 12, 24, …$ and find $a_{8}$.

Exercise 8 – Geometric with a fraction

A geometric sequence with ratio 1/2: each bar is half the one above.

The bars show $80, 40, 20, …$ with ratio $\frac{1}{2}$. Find $a_{6}$ for the sequence starting at 80.

Exercise 9 – Recursive geometric

Write the first four terms of $a_{1} = 2$, $a_{n} = 3a_{n-1}$.

Exercise 10 – Gauss's sum

Pairing the sequence with its reverse: every column sums to 11.

Find $1 + 2 + 3 + … + 100$ using the pairing idea shown for the numbers 1 to 10.

Exercises 11 and up

Exercise 11 – Arithmetic series

Find the sum of the first 20 terms of $5, 8, 11, …$.

Exercise 12 – Theater seats

A theater has 12 seats in the first row and each row has 2 more seats than the row before. There are 15 rows. How many seats are there?

Exercise 13 – Geometric series

Find the sum of the first 8 terms of $3 + 6 + 12 + …$.

Exercise 14 – Halving series

Find the sum of the first 7 terms of $64 + 32 + 16 + …$.

Exercise 15 – Doubling pennies

Pennies per day for the first five days.

Noah earns 1 cent on day 1, 2 cents on day 2, 4 cents on day 3, and keeps doubling. How many dollars has he earned in total after 30 days?

Exercise 16 – Savings plan

Mei deposits $200 at the end of each year into an account that earns 5% per year. The balance after 10 years is $200 + 200(1.05) + … + 200(1.05)^{9}$. Find it.

Exercise 17 – Triangular stack

A stack of logs with 5 in the bottom row.

A stack of logs has 20 logs in the bottom row, and each higher row has one fewer log, ending with 1 log. How many logs are in the stack? The picture shows a stack with 5 rows.

Exercise 18 – Fibonacci

A sequence has $a_{1} = 1$, $a_{2} = 1$, and $a_{n} = a_{n-1} + a_{n-2}$. Write the first 8 terms. Is it arithmetic or geometric?

Exercise 19 – Find the error

Aisha says $2, 4, 8, 16$ is arithmetic because it keeps increasing. Explain the error.

Exercise 20 – Two terms given

An arithmetic sequence has $a_{3} = 11$ and $a_{8} = 36$. Find $d$, $a_{1}$, and a formula.

Key facts behind this algebra 2 sequences series worksheet

Key facts

A sequence is a function whose domain is the positive integers.
Arithmetic: a_n = a_1 + (n – 1)d; geometric: a_n = a_1·r^(n-1).
Recursive formulas build each term from the previous one.
Arithmetic sum: S_n = n(a_1 + a_n)/2.
Geometric sum: S_n = a_1(1 – r^n)/(1 – r), r ≠ 1.

How to use this algebra 2 sequences series 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 algebra 2 sequences series worksheet as a PDF with the button below and keep it with your notes.

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