# Arithmetic and Geometric Sequences Worksheets

What is the Difference Between an Arithmetic and Geometric Sequence? A sequence is a set of numbers, which are called terms, arranged in some order. However, two of the sequences which are the easiest to solve are the arithmetic and geometric sequence. The arithmetic sequence works when you have to add or subtract the same value to get the next number in the sequence. For instance, if you have a sequence, 2, 5, 8, 11, 14, ... then you know that you have to add 3 to get the next number. On the other hand, in a geometric sequence, one term is always multiplied or divided by the same value to get the same number. For instance, if you have a sequence, 1, 2, 4, 8, 16,... then, each proceeding number is the multiple of 2 of the previous number.

• ### Basic Lesson

Guides students through Arithmetic and Geometric Sequences. To find any term of an arithmetic sequence: an = a1 + (n-1)d where a1 is the first term of the sequence, d is the common difference, n is the number of the term to find. To find the sum of a certain number of terms of an arithmetic sequence: Sn = n (a1+ an)2. where Sn is the sum of n terms (nth partial sum), a1 is the first term, an is the nth term.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of Arithmetic and Geometric Sequences. To find any term of a geometric sequence: an = a1 . rn - 1. where a1 is the first term of the sequence, r is the common ratio, n is the number of the term to find.

• ### Independent Practice 2

Students find the Arithmetic and Geometric Sequences in assorted problems. The answers can be found below. Find the d or r, an and Sn.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of Arithmetic and Geometric Sequences.

• ### Skill Quiz

This tests the students ability to evaluate Arithmetic and Geometric Sequences.