Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d...
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Transcript of Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d...
![Page 1: Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.](https://reader036.fdocuments.net/reader036/viewer/2022072011/56649e245503460f94b11d3e/html5/thumbnails/1.jpg)
Arithmetic Sequences Arithmetic Sequences and Seriesand Series
![Page 2: Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.](https://reader036.fdocuments.net/reader036/viewer/2022072011/56649e245503460f94b11d3e/html5/thumbnails/2.jpg)
A sequence is arithmetic if
each term – the previous term = d
where d is a constante.g. For the
sequence ...,8,6,4,2d = 2nd term – 1st
term= 3rd term – 2nd term . . . = 2
Arithmetic Sequence
The 1st term of an arithmetic sequence is
given the letter a.
![Page 3: Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.](https://reader036.fdocuments.net/reader036/viewer/2022072011/56649e245503460f94b11d3e/html5/thumbnails/3.jpg)
Arithmetic Sequence
An arithmetic sequence is of the form...,3,2,, dadadaa
Notice that the 4th term has 3d added so, for example, the 20th term will be
da 19
The nth term of an Arithmetic Sequence is dnaun )1(
An arithmetic sequence is sometimes called an Arithmetic Progression (A.P.)
![Page 4: Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.](https://reader036.fdocuments.net/reader036/viewer/2022072011/56649e245503460f94b11d3e/html5/thumbnails/4.jpg)
SUMMARY
)(2
lan
Sn
The sum of n terms of an arithmetic series
is given by
...,3,2,, dadadaa
An arithmetic sequence is of the form
The nth term is dnaun )1(
or
))1(2(2
dnan
Sn
![Page 5: Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.](https://reader036.fdocuments.net/reader036/viewer/2022072011/56649e245503460f94b11d3e/html5/thumbnails/5.jpg)
ExampleThe common difference of an arithmetic series
is -3 and the sum of the first 30 terms is 255. Find the 1st term.
Solution:
255303 30S and , nd
))1(2(2
dnan
S n
))3(292(2
30255 a
)872(15255 a
87215
255 a
52 aa28717