12.5 Sigma Notation and the nth term

1. 12.5 Sigma Notation and the nth term By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Assignment #45 No book assignment, instead it is a worksheet.

2. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. • Capitol Greek letter sigma • Sigma represents a Summation • The bottom it the start value, lower bound of summation • The top is the end value, upper bound of summation • The letter used in the lower bound of summation is called the index of summation Sigma Notation

3. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. This is an arithmetic series with common difference +3 This is a geometric series with common ratio Example 1: Expand the summation and describe the series

4. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. This is an arithmetic series with common difference -2 This is a geometric series with common ratio 2 Example 1: Expand the summation and describe the series

5. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. • Arithmetic Series • Geometric Series • Infinite Geometric series For our purposes you will only need to use the ARITHMETIC for sigma notation problems. Summation Formulas

6. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 2: Use the summation formula for ARITHMETIC series to find the sum

7. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 2: Use the summation formula for ARITHMETIC series to find the sum

8. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. • Move all terms to one side so that one side is zero • A quadratic has TWO solutions that can be found by… • X-box Factoring • Guess and Check factoring • Quadratic formula • Note: for Series • Do we have fractional terms? (e.g. first term, term?) • Do we have negative terms? (e.g. -4th term?) Solving Quadratic Equations

9. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 3: Find the number of terms needed to obtain the given sum

10. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 3: Find the number of terms needed to obtain the given sum

11. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 3: Find the number of terms needed to obtain the given sum

12. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. Example 3: Find the number of terms needed to obtain the given sum

13. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. • Find the number of terms (n) needed for the series below to have a sum of Summary

14. By the end of the section students will be able to expand a summation given in sigma notation, determine the sum of an arithmetic series using sigma notation and determine the number of terms in a arithmetic sequence for a given sum as evidenced by completion of an exit slip. • Find the number of terms (n) needed for the series below to have a sum of Summary