In these worksheets, students will work with arithmetic and geometric sequences.

#### An arithmetic sequence is a sequence of numbers in which the interval between the consecutive terms is constant. A geometric sequence is a sequence of numbers in which after the first term, consecutive ones are derived from multiplying the term before by a fixed, non-zero number called the common ratio. We come across the terms 'sequence' and 'series' very often in our lives. By sequence, we mean a list of things that obey a specific order. Series, on the other hand, is the arrangement of similar things one after the other, without following a fixed order. When talking about sequence and series in mathematics, a sequence is a collection of numbers that are placed, following a specific order with repetitions allowed. The series, on the other hand, is a process of adding infinitely many numbers without a fixed order. There are a variety of different types of these sequences and series. The most basic ones are arithmetic and geometric. So, what is the difference between these two basic types of sequences and series? The first difference is that the arithmetic sequence follows a constant difference between consecutive terms. In geometric sequence or series, there is a constant ratio being followed between consecutive terms. To find the next term in an arithmetic sequence, we use the following formula; tn = t1 - (n-1)d Here, t_1 is the first term of the sequence, n is the term number that we need to find, and d is the common difference between two consecutive terms. The common difference can be calculated by subtracting any two consecutive terms. To find the next term in a geometric sequence, we use the following formula; tn =t1 x r(n-1) Here, r is the common ratio between the consecutive terms. The ratio, r, can be calculated by dividing any two consecutive terms in the sequence.

These worksheets introduce the concepts of arithmetic and geometric series. In these worksheets, students will determine if a series is arithmetic or geometric. They will find the common difference in arithmetic sequences. They will find the common ratio in geometric sequences. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also includes ample worksheets for students to practice independently. When finished with this set of worksheets, students will be able to recognize arithmetic and geometric sequences and calculate the common difference and common ratio. These worksheets explain how to use arithmetic and geometric sequences and series to solve problems. Sample problems are solved and practice problems are provided.

# Arithmetic and Geometric Sequences and Series Worksheets

## Arithmetic and Geometric Sequences and Series Lesson

This worksheet explains the differences and use of arithmetic and geometric sequence and series to solve for terms. A sample problem is solved, and two practice problems are provided.

## Lesson and Practice

This sheet will walk students through this problem: Find the sum of the first 5 term of the sequence 2, 4, 6, 8, ...

## Worksheet

Students will use arithmetic and geometric sequences and series to solve problems. Ten problems are provided.

## Practice

We will work on these problems in a variety of ways.

## Review

The concept of how to use arithmetic and geometric sequences and series to solve problems is reviewed. A sample problem is solved and six practice problems are provided.

## Quiz

Students will demonstrate their proficiency with these concepts and skills. Ten problems are provided.

## Check

For each series you will find the d or r, an and Sn. Three problems are provided, and space is included for students to copy the correct answer when given.