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 * Aim: How do we find the sum of n terms of an arithmetic series?** //(This formula is given on the Regents Reference Sheet as the **Sum of a Finite Arithmetic Series**)//

At the end of the lesson, you will be able to...


 * 1) define series and arithmetic series
 * 2) compare and contrast arithmetic sequence and arithmetic series
 * 3) explore the formula for finding the sum of the first n terms of an arithmetic series
 * 4) apply the formula to problems when given a sum or described verbally

Here are some questions for you to answer in your notebook as you watch the videos.


 * 1) What is an arithmetic series?
 * 2) What is the difference between and arithmetic series and an arithmetic sequence?
 * 3) Write the formulas used for an arithmetic series. (There are two)
 * 4) How do the formulas differ?

[|Video 1]

[|Video 2]


 * Classwork:** Answer the following questions
 * 1) Find the sum of the first 15 terms of the arithmetic series 1 + 4 + 7 + ... (Ans: 330)
 * 2) The sum of the first and last terms of an arithmetic sequence is 80 and the sum of all the terms is 1200. How many terms are in the sequence? (Ans: 30)


 * Homework:** Do problems 3-17 odd, 25, 27, 29, and 31. **Any directions that say "Write in sigma notation" ignore.**

[|Arith_Series.JPG]


 * Answers:**

[|A-Arith_Series.JPG]


 * Journal entry:** Describe how to quickly find the sum of all natural numbers from 1 to 100. Explain why your method works.