Math521B_Chp1_2_W2017_wNotes.notebook

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February 09, 2017

Chp. 1.2 Arithmetic SeriesAt age 10 his teacher challenged the class

Find the sum of the numbers from 1 to 100

Gauss blew them all away and found it in only a few minutes (no calculator)!

How?!?

Arithmetic Series: the sum of all the terms from an arithmetic series

***You have t1, n and d******You have t1, tn and n ***

t1=first term

n = # of terms

d = common difference

tn = nth term

Sn = sum of first n terms

Math521B_Chp1_2_W2017_wNotes.notebook

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February 09, 2017

Arithmetic Sequence Vs. Arithmetic Series

2, 4, 6, 8 2 + 4 + 6 + 8

LISTING out all the terms one by one ADDING all the terms together

Ex. 1) Find the sum of the first 24 terms of the following series:

10 + 12 + 14 + 16 + ...

Ex. 2) Determine the sum of the following series:

72 + 65 + 58 + 51 + ... -5

or

Ex. 3) For the arithmetic series' described below:

a) Find t1 if:

d = 4, n = 9, Sn = 243

b) Find n if:

t1 = 25, tn = -8, Sn = 102

Math521B_Chp1_2_W2017_wNotes.notebook

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February 09, 2017

Ex. 4) The Sum of the first two terms of an arithmetic sequence is 19 and the sum of the first four terms is 50. What are the first six terms of the series and the sum to 20 terms?

Complete Exercises p. 27 - 31 # 1, 2, 4 (a, b), 5, 6 (a, c), 9, 11, 13, 20