Precalculus Sequences and Series Worksheet (PDF)

Precalculus math worksheet: Sequences and Series – Maths PDF

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

These 20 problems practice sequences and series (Common Core F-IF.A.3, F-BF.A.2 and A-SSE.B.4). You will write explicit and recursive formulas, find finite sums, use sigma notation and evaluate infinite geometric series.

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

Precalculus sequences series worksheet: exercises 1 to 10

Exercise 1 – List terms

Write the first four terms of $a_{n}=5+3(n-1)$.

Exercise 2 – Explicit arithmetic formula

The sequence 7, 11, 15, 19, …

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

Exercise 3 – Formula from two terms

An arithmetic sequence has $a_{3}=10$ and $a_{8}=25$. Find $a_{n}$.

Exercise 4 – Geometric formula

The sequence 3, 6, 12, 24, …

Write an explicit formula for $3,6,12,24,\text{ … }$ and find $a_{10}$.

Exercise 5 – Fractional ratio

Find the common ratio and the sixth term of the sequence $81,27,9,3,\text{ … }$.

Exercise 6 – Recursive sequence

Let $a_{1}=2$ and $a_{n}=3a_{n-1}-1$. Find $a_{2},a_{3},a_{4}$.

Exercise 7 – Recursive to explicit

A sequence has $a_{1}=5$ and $a_{n}=a_{n-1}+4$. Write an explicit formula.

Exercise 8 – Sum of the first 100 integers

Find $1+2+3+\text{ … }+100$.

Exercise 9 – Arithmetic series

Find the sum of the first $30$ terms of $5,8,11,\text{ … }$.

Exercise 10 – Sum of 20 terms

Find the sum of the first $20$ terms of $7,11,15,\text{ … }$.

Exercises 11 and up

Exercise 11 – Sigma notation

Evaluate $\sum_{k=1}^{5}(2k+1)$.

Exercise 12 – Sigma with an arithmetic formula

Evaluate $\sum_{k=1}^{40}(3k-2)$.

Exercise 13 – Geometric series

Find $2+6+18+\text{ … }$ (6 terms).

Exercise 14 – Partial sum of a convergent series

Partial sums of a series approaching a limit.

Find the sum of the first 8 terms of $1+\frac12+\frac14+\text{ … }$.

Exercise 15 – Infinite geometric series

A bar split into halves.

Find the sum of $8+4+2+1+\text{ … }$.

Exercise 16 – Sigma with infinity

Evaluate $\sum_{k=1}^{\infty}3(0.4)^{k-1}$.

Exercise 17 – Converge or diverge?

Decide whether each series has a sum, and find it if it does: (a) $2+6+18+\text{ … }$; (b) $5-\frac52+\frac54-\text{ … }$.

Exercise 18 – Repeating decimal

Write $0.\overline{36}$ as a fraction using a geometric series.

Exercise 19 – Salary

Priya’s starting salary is $\$42{,}000$ and she gets a $\$2{,}000$ raise each year. Find her salary in year 10 and her total earnings over 10 years.

Exercise 20 – Bouncing ball

A ball bouncing to 60 percent each time.

A ball is dropped from $10$ ft and bounces up to $60\%$ of its previous height each time. Find the total distance it travels (up and down) before coming to rest.

Exercise 21 – Doubling pennies

On day 1 Noah saves $1$ cent, and each day he saves double the previous day. How many dollars has he saved after 20 days?

Key facts behind this precalculus sequences series worksheet

Key facts

Arithmetic: a_n = a_1 + (n – 1)d; sum S_n = (n/2)(a_1 + a_n).
Geometric: a_n = a_1 r^(n-1); sum S_n = a_1(1 – r^n)/(1 – r).
Sigma notation adds the terms from the lower index to the upper index.
An infinite geometric series converges only if |r| < 1, and then S = a_1/(1 - r).
A recursive formula gives each term from the one before it.

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

All Precalculus chapters: Precalculus math.

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