(9)ArithmeticSequences(1).notebook
Definition
:A
sequence
isasetofnumbersinaspecificorder.
2,5,8,….isanexampleofasequence.
Note:
Asequencemayhaveeitherafiniteoraninfinitenumberof
terms.
Sequences
The
terms
ofasequencearetheindividualnumbersinthesequence.
Ifwelet
a
1
representthefirsttermofasequence
,
a
n
representthen
th
term
,and
nrepresentthetermnumber
,
thenthesequenceisrepresentedbya
1
,a
2
,a
3
,….,a
n
,…
2,5,8,11,14,....
Intheexampleabove,a
1
=2,a
2
=5,a
3
=8,etc.
Example:Writethefirst3termsofeach
sequence.
1.a
n
=n
2
+2
Start by plugging in n = 1, then n=
2, etc. Write the terms as a
sequence.
2.a
n
=(n+1)(n+2)
a
1
=1
2
+2
a
1
=1+2
a
1
=3
a
2
=2
2
+2
a
2
=4+2
a
2
=6
a
3
=3
2
+2
a
3
=9+2
a
3
=11
3,6,11
a
1
=(1+1)(1+2)
a
1
=(2)(3)
a
1
=6
a
2
=(2+1)(2+2)
a
2
=(3)(4)
a
2
=12
a
3
=(3+1)(3+2)
a
3
=(4)(5)
a
3
=20
6,12,20
ArithmeticSequences
Definition
:An
arithmeticsequence
isasequencein
whicheachterm,afterthefirst,isthe
sum
ofthe
precedingtermandacommondifference.
Example
:Inthesequence2,5,8,11,14,......
Thisisanarithmeticsequencebecauseto
geteachnumberinthesequence,weadd3.
So,wesaythe
commondifference
is3.
Practice:
Determineifthesequencesbelowarearithmeticsequences.
Ifyes,determinethecommondifference.
1.)2,3,8,…..
2.)5,9,13,…..
3.)1,7,14,……
4.)5,1,7,…….
5.)3,5,8,......
6.)9x,2x,5x,…….
REMEMBER:a
1
=2a
2
=5a
3
=8etc.ANDd=3
(TIP:figureoutifthesamenumberisbeingaddedoverandoveragain)
Thisisanarithmetic
sequencebecause
5isaddedtothefirst
termtodetermine
thesecondterm,
5isaddedtothe
secondtermto
determinethe
thirdterm,etc
d=5
arithmeticsequence
d=4
notan
arithmeticsequence
6isaddedtofind
thesecondtermand
then7isaddedtofind
thethirdterm
arithmeticsequence
d=6
arithmeticsequence
d=7x
notan
arithmeticsequence
+
3
+
3
+
3
+
3
+
3
