September 22, 2017

Warm UpRecall: an = a1 + (n - 1)d

Multiple Choice: Given the arithmetic sequence below 2, 7, 12, 17, 22, 27,….

What term in the sequence is equal to 137?

A) 28th term

B) 27th term

C) 26th term

D) 25th term

Algebra 2 9.4 Arithmetic Series

September 22, 2017

Series Task: There are 10 rows of seats in an auditorium. Each consecutive row of seats has one additional seat added on to each end. The first row contains 15 seats, and, therefore, the second row has 17 seats. How many seats are in the seventh row?

September 22, 2017

Part Two:How many seats are in the auditorium in all? Explain your thought process using a picture, words, or algebraic reasoning.

September 22, 2017

Example 1:

Definition: A series is the sum of the terms of a sequence.

Arithmetic Sequence vs. Arithmetic Series

18, 22, 26, 30 18 + 22 + 26 + 30

September 22, 2017

Two Formulas for Arithmetic Series

September 22, 2017

Example 2: Find the sum of the first 100 positive integers.

September 22, 2017

Example 3: What is the sum of the even integers from 2 to 100?

September 22, 2017

Example 4: Find the sum of the first 20 even integers beginning with 2.

September 22, 2017

Example 5:

September 22, 2017

Example 6: What is the sum of the finite arithmetic series,4+9+14+19+24+ ..... +99?

September 22, 2017

Example 7:

September 22, 2017

Sigma Notation

First value to put in for n

Last value to put in for n

Formula for the series

September 22, 2017

Evaluating sums in sigma notationExample 8: Evaluate the following.

b)

September 22, 2017

d) e) f)

September 22, 2017

Example 9: Evaluate the following.

a) b)

September 22, 2017