Lesson: Arithmetic Series Mathematics • 10th Grade

In this lesson, we will learn how to calculate the sum of the terms in an arithmetic sequence with a definite number of terms.

Lesson Plan

Students will be able to

recognize the formula for the sum of an arithmetic sequence in terms of the first and last terms,
recognize the formula for the sum of an arithmetic sequence in terms of its first term and common difference,
find the sum of arithmetic sequences with a given number of terms, including a given range of terms, and examples where you know the first and last terms, and the first term and the common difference (or have the information to calculate these),
solve applied problems, including finding the number of terms given the sum and other necessary information.

Q1:

Find the number of terms in the arithmetic sequence whose first term is 11 and last term is 81, where the sum of all the terms is 506.

Q2:

Find an expression for the sum of an arithmetic sequence whose first term is and whose common difference is .

Q3:

Write an expression for the sum of the first terms of an arithmetic sequence with first term and last term .