Presentation on theme: "Warm UP! 1.Indentify the following as Arithmetic, Geometric, or neither: a.2, 5, 8, 11, … b.b. 2, 6, 24, … c.c. 5, 10, 20, 40, … 2. Demonstrate you know."— Presentation transcript:
Warm UP! 1.Indentify the following as Arithmetic, Geometric, or neither: a.2, 5, 8, 11, … b.b. 2, 6, 24, … c.c. 5, 10, 20, 40, … 2. Demonstrate you know the difference in an arithmetic series and sequence by writing one of each. Both should have a first term of 2 and common difference of Find the 50 th term of the sequence a n = 2n – 6
Summation Notation AKA Sigma Notation i = Index of Summation (lower limit) n = upper limit
Partial Sum of an Arithmetic Series The sum of the terms from 1 to n of an arithmetic sequence can be found using this formula: n=number of terms
nth Partial Sum The sum of the first n terms of an infinite sequence is called the nth partial sum.
Example: Find the Sum Find the sum:
Example: Find the Sum Find the sum of the integers from 1 to 100.
Example: Find the Sum Find the sum: …+5 860
Find the 78 th partial sum:
Evaluate the sum:
Example 6: Sigma Notation
Example: Find the Partial Sum Find the 150 th partial sum of the AS. – 5,16,27,38,49,…
Example: An A.S. has a 1 = 19 and a 2 = 32 1.Find the common difference 2.Find a Find S Find n if a n = Find n if S n = , ,
Example: Applications An auditorium has 20 rows of seats. There are 20 seats in the 1 st row, 21 seats in the second row, 22 seats in the 3 rd row, and so on. How many seats are there in all 20 rows?
Example: Applications A small business sells $10,000 worth of products during its first year. The owner of the business has set a goal of increasing annual sales by $7500 each year for 19 years. Assuming that this goal is met, find the total sales during the first 20 years this business is in operation.
Example: Applications Shelbi starts an exercise program. At the first workout she does 5 push ups. The next workout she does 8 push ups. She decides to let the number of push ups in each workout be a term in a sequence. Find the number of pushups she does on the tenth workout. Also, find the total number of pushups she has done after 10 workouts
sum of a finite geometric series
Ex. 6 Find the sum: = 5.714
Ex. 6 Find the sum: = 98,301
Find the sum of the first 60 terms of the sequence: a n = -3( 2 ) n-1 = -49,149