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7/21/2019 Series and Sequences
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serieand
SEQUENCES
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-in mathematics, is a stringof objects, like numbers,that follow a particular
pattern. he indi!idualelements in a se"uenceare called terms.
SEQUENCE
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- is a list of things #usuall$numbers% that are in order.-some of the simplest
se"uences can be found inmultiplication tables&
SEQUENCE
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e'amples
(, ), *, +, +, +, +, /0attern& 1add ( to the pre!ious number toget the ne't number23, +, 4, (), 4, )3, 5, /0attern& 1add + to the pre!ious numberto get the ne't number2
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e'amples
+3,6 ,7 +),6 +4,7 ,6 ),7 ,/0attern& 1alternatingl$ subtract andmultipl$ b$ to get the ne't number23,8 ,84 ),8) +,8 3,8+3 (3,8+ 4,/0attern& 1add increasing e!en numbers to
get the ne't number2
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in9nite
SEQUENCE
:hen the se"uence goes on fore!er it iscalled an infnite sequence,
otherwise it is a fnite sequence
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e'amples
<+, , (, 4, ...= is a !er$ simple se"uence#and it is an in9nite se"uence%<3, , (3, (, ...= is also an in9nitese"uence<+, (, , 5= is the se"uence of the 9rst 4odd numbers #and is a 9nite se"uence%
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e'amples
<+, , 4, , +), (, ...= is an in9nitese"uence where e!er$ term doubles<a, b, c, d, e= is the se"uence of the 9rst letters alphabeticall$
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arithmeticSEQUENCE
>n an arithmetic se"uence, the di?erencebetween consecuti!e terms is constant. he constant di?erence is denoted b$ d.
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e'amples
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e'amples
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