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Sequences & Series
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Sequences & Series
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Sequences & Series
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the Arithmetic Sequence formula to find n, a1<=
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or an.
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Sequences & Series
![](3D"slide0011_image040.png")
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Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
=
Click to edit Master title style
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
‹#›
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Sequences & Series
Patterns in Numbers & Nature
Sequences
]A list of numbers
]Has two forms
<=
/div>
<=
span
class=3DB1B style=3D'position:absolute;left:-4.97%'>]Arithmetic
=
;
<=
span
class=3DB2B style=3D'position:absolute;left:-3.92%'>]Each number is
separated by a common difference
<=
span
class=3DB1B style=3D'position:absolute;left:-4.97%'>]Geometric
=
<=
span
class=3DB2B style=3D'position:absolute;left:-4.32%'>]Each number is
multiplied by a common ratio
Te=
rm of
a Sequence
lThe subscript n tells
you which term in the sequence it is
lThe expression finds
the term
lFind the first 5 terms
a1
a2
=
;
a3
=
;
a4
=
;
a5
Factorials
<=
span
class=3DBB style=3D'position:absolute;left:-4.36%'>]The factorial o=
f a
number is the multiplication of the number and each number befor=
e it
down to 1
<=
span
class=3DBB style=3D'position:absolute;left:-5.21%'>]Example
<=
span
class=3DB1B style=3D'position:absolute;left:-4.79%'>]5! =3D 5*4*3*2=
*1
Summation Notation
]Means to “sum up”
]“i”
is the index of summation
]“i”
is starting value (lower limit of summation)=
]“n” is ending value (upper limit of summation)
Se=
ries
with Summation Notation
lA finite series is a list terms from a =
sequence
that is added up
lAn infinite series goes on forever
l<=
span
style=3D'mso-special-format:lastCR;display:none'>
Series
]The SUM of a list of
numbers
]Has two forms
<=
/div>
<=
span
class=3DB1B style=3D'position:absolute;left:-4.97%'>]Arithmetic
=
;
<=
span
class=3DB1B style=3D'position:absolute;left:-4.97%'>]Geometric
Arithmetic Sequences
<=
span
class=3DB1B style=3D'position:absolute;left:-8.92%'>]Common differe=
nce is positive
<=
span
class=3DB1B style=3D'position:absolute;left:-8.92%'>]Common differe=
nce is negative
Find the 31st term of =
this
sequence 4 + 7 + 10 + 13….
The 31st term is =
94
Arithmetic Series
Find the sum of 5 + 8 + 11 + 14 + …=
.+
62
(Hint: use previous formula first)
Writing in Sigma Notation (Arithmetic)
<=
span
style=3D'font-size:88%'>]Find common difference
]
<=
span
style=3D'font-size:88%'>]Make that the coefficient of n
]
<=
span
style=3D'font-size:88%'>]Solve for 1st term
<=
span
style=3D'font-size:88%'>]Put it all together
5
5(1) + =
? =3D
47
? =3D 4=
2
Try Example
5 + =
2 + -1
+ -4