12.5 Sigma Notation and the nth term
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Transcript of 12.5 Sigma Notation and the nth term
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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.
*12.5 Sigma Notation and the nth term
Assignment #45No book assignment, instead it is a worksheet.
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Sigma Notation*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
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.
![Page 3: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/3.jpg)
Example 1: Expand the summation and describe the series
A.
This is an arithmetic series with common difference +3
B.
This is a geometric series with common ratio
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.
![Page 4: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/4.jpg)
Example 1: Expand the summation and describe the series
C.
This is an arithmetic series with common difference -2D.
This is a geometric series with common ratio 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.
![Page 5: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/5.jpg)
Summation Formulas*Arithmetic Series
*Geometric Series
*Infinite Geometric series
For our purposes you will only need to use the ARITHMETIC for sigma notation problems.
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.
![Page 6: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/6.jpg)
Example 2: Use the summation formula for ARITHMETIC series to find the sum
A.
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.
B.
![Page 7: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/7.jpg)
Example 2: Use the summation formula for ARITHMETIC series to find the sum
C.
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.
D.
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Solving Quadratic Equations*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?)
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.
![Page 9: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/9.jpg)
Example 3: Find the number of terms needed to obtain the given sum
A.
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.
![Page 10: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/10.jpg)
Example 3: Find the number of terms needed to obtain the given sum
B.
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.
![Page 11: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/11.jpg)
Example 3: Find the number of terms needed to obtain the given sum
C.
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.
![Page 12: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/12.jpg)
Example 3: Find the number of terms needed to obtain the given sum
D.
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.
![Page 13: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/13.jpg)
Summary1. Find the number of terms (n) needed for the
series below to have a sum of
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.
![Page 14: 12.5 Sigma Notation and the nth term](https://reader033.fdocuments.in/reader033/viewer/2022061502/56816109550346895dd053a4/html5/thumbnails/14.jpg)
Summary1. Find the number of terms (n) needed for the
series below to have a sum of
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.