Algebra 2 9.4 Arithmetic Series

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?

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

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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

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Two Formulas for Arithmetic Series

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

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

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

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Example 5:

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

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Example 7:

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Sigma Notation

First value to put in for n

Last value to put in for n

Formula for the series

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Evaluating sums in sigma notationExample 8: Evaluate the following.

b)

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d) e) f)

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Example 9: Evaluate the following.

a) b)

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