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 ....