Willow Tree
Arithmetic and Geometric Sequences
Old mathematicians never die; they just lose some of their functions. Studying sequences gives scholars an opportunity to use a new notation. Learners write functions to model arithmetic and geometric sequences and use them to find new...
EngageNY
Integer Sequences—Should You Believe in Patterns?
Help your class discover possible patterns in a sequence of numbers and then write an equation with a lesson that covers sequence notation and function notation. Graphs are used to represent the number patterns.
Willow Tree
Fibonacci and Other Sequences
Fibonacci is an interesting sequence that forms some unique patterns. Learners explore sequences that do not have the typical arithmetic and geometric patterns. They identify the pattern and find the next consecutive terms....
Curated OER
Arithmetic Sequences
Find the sequence of an equation with your math super stars. They differentiate between arithmetic and geometric sequences and then calculate the sum of finite and infinite sequences.
Curated OER
Arithmetic Sequences
Twenty-eight problems, two pages, and an answer key all related to number patterns, recursive formula, and arithmetic sequence. Leaners find the next number in the pattern or sequence and determine the arithmetic formula to go with the...
Curated OER
Geometric Sequences
Explore geometric sequences with this 30 problem learning exercise. Upper graders determine if the sequences shown are geometric and find the common ratio. Then, given the explicit formula for a geometric sequence find the first five...
Curated OER
Introduction to Infinite Sequences
In this infinite sequences worksheet, students discover the convergence and divergent behavior of infinite sequences. This worksheet references L'Hopital's rule.
Curated OER
Exploring Infinite Sequences, Part II
In this algebra worksheet, students identify the nth term of the sequence. They find the missing term in the pattern and what theorem justifies their choice. There are 12 questions.
Virginia Department of Education
Arithmetic and Geometric Sequences and Series
Examine the importance of sequence and series through contextual situations. Here, learners partake in a five-day unit that begins with the basics of arithmetic and geometric sequences and series. As it progresses, pupils apply the...
Curated OER
Comparing Arithmetic and Geometric Sequences
In this algebra worksheet, students analyze patterns and identify it as arithmetic, geometric, or neither. There are 30 questions with answers.
Curated OER
Infinite Geometric Series
In this geometric series instructional activity, students examine a given geometric series to determine if the series converges or divergeas. They evaluate and determine the common ratio of a geometric series. This four-page...
Curated OER
Converge or Diverge?
Young scholars prepare for the calculus concepts of limits by examining sequences that converge and diverge. By using an Excel program that generates sequences, students manipulate the starting number, multiplier and add-on values, and...
Teach Engineering
The Fibonacci Sequence and Robots
What better way to introduce the idea of a sequence than with robots! An educational lesson explains the classic Fibonacci sequence before pupils build and program a robot to move. Additionally, the lesson challenges individuals to...
CK-12 Foundation
Sequence of Partial Sums: Partial Sums
Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...
Curated OER
Finding The Sum of an Infinite Series
Students examine finding the sum of an infinite series as the limit of partial sums. Through hands-on activities, students create their own sequence by finding the area of a square and then cutting it in half-sized pieces. They write...
Curated OER
Sequences and Series
For this sequences and series worksheet, 10th graders solve and complete 13 different problems that include infinite geometric series. First, they find the sum of each infinite geometric series. Then, students find the first three terms...
Curated OER
Summary Worksheet: Sequences
In this sequence worksheet, students determine whether the sequence is convergent or divergent. They find the limit of a given sequence, and solve distance problems. Students explore partial sums of an infinite series and use the...
Curated OER
Trig Functions
In this trig functions worksheet, students solve and complete 24 different types of problems. First, they find the limits for each trig function given. Then, students find xso that the given infinities series converges. They also find...
Curated OER
Introduction to Infinite Series
In this algebra worksheet, students find the pattern and nth formula for different series. They decide whether a sequence will diverge or converge. There are 13 questions.
Curated OER
Sequences
In this trigonometry worksheet, learners write formulas for sequences using a given pattern. There are 12 questions with an answer key.
West Contra Costa Unified School District
Arithmetic Series
Fall for a series. Learners determine how to find out how far a skydiver falls in the first 20 seconds. The Algebra II lesson introduces the idea of adding up the terms of an arithmetic sequence. Pupils learn how to use Sigma notation to...
Curated OER
Sum of Infinite Geometric Series
Your mathematicians solve problems using geometric series in this pre-calculus lesson. They divide a unit square into very small pieces and identify the reasoning behind the sum of a series being less than one.
Curated OER
Exploring Infinite Series
Learners analyze geometric series in detail. They determine convergence and sum of geometric series, identify a series that satisfies the alternating series test and utilize a graphing handheld to approximate the sum of a series.
Curated OER
Finite Geometric Series
In this geometric series learning exercise, students find the nth term in a sequence. They evaluate a given geometric sequence and determine the number of terms in a geometric series. This two-page learning exercise contains 26...