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SEQUENCES & SERIES
Miguel Pérez Fontenla, Nov 2009
1,2,3,4,5,.....
...6,7,8,......
n
Natural numbers
2,4,6,8,.....
...10,12,14......
Even numbers
2n
1,3,5,7,.....
...9,11,13......
Odd numbers
2 1n
4,7,10,13,.....
...16,19,22......
Multiple of three plus one
3 1n
2,4,8,16,.....
...32,64,128.....
Powers of two
2n
1,2,4,8,16,.....
...32,64,128.....
Powers of two
12
n
1,3,9,27,.....
...81,243,.....
Powers of three
13
n
2,5,10,17,.....
...26,37,.....
n squared plus one
21n
1,8,27,64,.....
...125,216,.....
n cubed
3n
2,6,12,20,.....
...56,72,90,.....
n multiplied by n minus one
1n n
1 1 3, , , ....
2 2 2
2 3
2
n
5 7 9..., , , , ....
2 2 2
two times n minus three divided by two
-1,1,-1,1,.....
...-1,1,-1,1,.....
minus one to the power of n
1n
1,-1,1,-1,.....
...1,-1,1,-1,.....
minus one to the power of n plus one
1
1n
two times n divided by two times n minus one
2 4 6 8, , , ....
1 3 5 7
10 12 14..., , , , ....
9 11 13
2
2 1
n
n
and....
Other series not so easy
1,0,1,0,1.....
...0,1,0,1.....1
1 if n odd 1 1
0 if n even 2
n
na
1,1,2,3,5.....
...8,13,21,.....
Fibonacci Sequence
1 2
1 if n = 1
if n > 1n
n n
aa a
81,27,9,.....
...3,1,1/3,.....
on divided by 3 to the power of n minus five
5
1
3n
2,3,5,7,11,.....
...13,17,19,23.....
prime numbers
0,1,4,6,8,9,10,.....
...12,14,15,16.....
no prime numbers
2,-4,6,-8.....
...10,-12,14,...
minus one to the power of n plus one multiplied by two times n
1
1 2n
n
two thirds to the power of n minus five
81 27 9 3, , , , ...
16 8 4 2
5
2 4 8 21, , , ...
3 9 16 3
n
two tine 2 squared to the power of n minus onedivided by four
1 2, , 2, ...
4 2
1
2 2
4 2 ,16, 32 2 , ...4
n
and now....
Funny series
a,b,d,g,k.....
...p,v,...
following the sequence 1,2,4,7,11,16,22
O,T,T,F,F,S,S.....
...,E,N,T
One, two, three, four, five,six, seven, eight, nine, ten....
M,T,W,T,F.....
...S,S
Week days
M,V,E,M,J.....
...S,N,U,P
Planets Solar SystemMercury, Venus, Earth, Mars, Jupiter, Saturn, Neptune, Uranus,
Pluto
F,S,T,F,F,S,S..... ,E,N,T
J,F,M,A,M,J,J........,A,S,O,N,D
31,28,31,30,31,...
...30,31,31,..Lengths of months in days
2,2,4,4,2,6,6,2,8,...
...8,2,10,...Table of two
5,4,2,9,8,6,...
...7,3,1Alphabetic Order In Spanish
2,10,12,16,17,18,19,200...
...201,202,..
In Spanish they start by the “D” letter:Dos, diez, doce, dieciseis,
diecisiete,dieciocho,diecinueve,doscientos....
2,3,6,16,22,23,26,32,33...
...36,42,43,46,..
In Spanish they finish with the “S” letter:Dos, tres, seis, dieciseis, veintidos, veintitres, veintiseis,
treinta y dos ....
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