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Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries...
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Transcript of Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries...
![Page 1: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/1.jpg)
Arithmetic Series
![Page 2: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/2.jpg)
A series is the expression for the sum of the terms of a sequence.
Sequence Series6, 9, 12, 15, 18
6+9+12+15+18
3, 7, 11, 15, ... 3+7+11+15+...
![Page 3: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/3.jpg)
Evaluate the seriesEx. 2, 11, 20, 29, 38, 472+11+20+29+38+47 = 147Ex. 100, 125, 150, 175, 200, 225100+125+150+175+200+225 = 975
![Page 4: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/4.jpg)
An arithmetic series is a series whose terms form an arithmetic sequence. We have a formula for evaluating an arithmetic series easily.
a1+a2+a3+...+an = (a1+an)n2
Hint: a1 is the first term in the seriesan is the last term in the seriesn is the number of terms in the series
![Page 5: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/5.jpg)
Evaluate the series using the formulaEx. 2, 11, 20, 29, 38, 47( )(2+47) = 147Ex. 100, 125, 150, 175, 200, 225 ( )(100+225) = 97562
62
![Page 6: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/6.jpg)
Another way to write a series is called summation notation. Ʃ is the Greek letter sigma.
Ʃ
(5n+1)
n=1
n=3
explicit formula for the sequence
greatest value of n, the number of terms
least value of n,usually n=1
![Page 7: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/7.jpg)
Write the explicit formula for the series 3+6+9+...for 33 terms.
sequence term n=#of term What do you have to do to n to get the sequence term?
3 1 n=1 3*1=3 so, 3n
6 2 n=2 3*2=6 so, 3n
9 3 n=3 3*3=9, so, 3n
![Page 8: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/8.jpg)
Write the summation notation to write the series 3+6+9+...for 33 terms.
Ʃ
3n
n=1
n=33
![Page 9: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/9.jpg)
Use the series Ʃ(5n+1).a. Find the number of terms in the series.
b. Find the first and last terms of the series.
c. Evaluate the series.
n=1
3
Since the values of n go from 1 to 3. There are three terms because n=1, n=2, and n=3.
The first term is n=1, so 5(1)+1=6. The last term is n=3, so 5(3)+1=16
1st term = 62nd term = 113rd term = 16
6+11+16 = 33
![Page 10: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/10.jpg)
Using the calculator to evaluate the series.
Steps:1. Select MATH2. Select 0:summation Ʃ(3. Enter the information in4. Hint ENTER
![Page 11: Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...](https://reader036.fdocuments.in/reader036/viewer/2022082818/56649ef65503460f94c0a641/html5/thumbnails/11.jpg)