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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
