SEQUENCES & SERIES Miguel Pérez Fontenla, Nov 2009
1,2,3,4,5,.....
1,2,3,4,5,..... ...6,7,8,......
1,2,3,4,5,..... ...6,7,8,......
1,2,3,4,5,..... ...6,7,8,...... Natural numbers
2,4,6,8,.....
2,4,6,8,..... ...10,12,14......
2,4,6,8,..... ...10,12,14......
2,4,6,8,..... ...10,12,14...... Even numbers
1,3,5,7,.....
1,3,5,7,..... ...9,11,13......
1,3,5,7,..... ...9,11,13......
1,3,5,7,..... ...9,11,13...... Odd numbers
4,7,10,13,.....
4,7,10,13,..... ...16,19,22......
4,7,10,13,..... ...16,19,22......
4,7,10,13,..... ...16,19,22...... Multiple of three plus one
2,4,8,16,.....
2,4,8,16,..... ...32,64,128.....
2,4,8,16,..... ...32,64,128.....
2,4,8,16,..... ...32,64,128..... Powers of two
1,2,4,8,16,.....
1,2,4,8,16,..... ...32,64,128.....
1,2,4,8,16,..... ...32,64,128.....
1,2,4,8,16,..... ...32,64,128..... Powers of two
1,3,9,27,.....
1,3,9,27,..... ...81,243,.....
1,3,9,27,..... ...81,243,.....
1,3,9,27,..... ...81,243,..... Powers of three
2,5,10,17,.....
2,5,10,17,..... ...26,37,.....
2,5,10,17,..... ...26,37,.....
2,5,10,17,..... ...26,37,..... n squared plus one
1,8,27,64,.....
1,8,27,64,..... ...125,216,.....
1,8,27,64,..... ...125,216,.....
1,8,27,64,..... ...125,216,..... n cubed
2,6,12,20,.....
2,6,12,20,..... ...,30,42,56,.....
2,6,12,20,..... ...,30,42,56,.....
2,6,12,20,..... ...,30,42,56,..... n multiplied by n plus one
 
 
 
two times n minus three divided by two
-1,1,-1,1,..... ...-1,1,-1,1,..... minus one to the power of n
1,-1,1,-1,.....
1,-1,1,-1,..... ...1,-1,1,-1,.....
1,-1,1,-1,..... ...1,-1,1,-1,.....
1,-1,1,-1,..... ...1,-1,1,-1,..... minus one to the power of n plus one
 
 
 
two times n divided by two times n minus one
and.... Other series  not so easy
1,0,1,0,1.....
1,0,1,0,1..... ...0,1,0,1.....
1,0,1,0,1..... ...0,1,0,1.....
1,1,2,3,5.....
1,1,2,3,5..... ...8,13,21,..... Fibonacci  Sequence
1,1,2,3,5..... ...8,13,21,..... Fibonacci  Sequence
81,27,9,.....
81,27,9,..... ...3,1,1/3,.....
81,27,9,..... ...3,1,1/3,.....
81,27,9,..... ...3,1,1/3,..... on divided by 3 to the power of n minus five
2,3,5,7,11,.....
2,3,5,7,11,..... ...13,17,19,23..... prime numbers
0,1,4,6,8,9,10,.....
0,1,4,6,8,9,10,..... ...12,14,15,16..... no prime numbers
2,-4,6,-8.....
2,-4,6,-8..... ...10,-12,14,...
2,-4,6,-8..... ...10,-12,14,...
2,-4,6,-8..... ...10,-12,14,... minus one to the power of n plus one multiplied by two times n
 
two thirds to the power of n minus five
 
 
two tine 2 squared to the power of n minus one divided by four
and now.... Funny series
a,b,d,g,k.....
a,b,d,g,k..... ...p,v,... following the sequence 1,2,4,7,11,16,22
O,T,T,F,F,S,S.....
O,T,T,F,F,S,S..... ...,E,N,T
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.....
M,T,W,T,F..... ...S,S Week days
M,V,E,M,J.....
M,V,E,M,J..... ...S,N,U,P Planets Solar System Mercury, Venus, Earth, Mars, Jupiter, Saturn,  Neptune, Uranus, Pluto
F,S,T,F,F,S,S.....
F,S,T,F,F,S,S..... ,E,N,T
J,F,M,A,M,J,J.....
J,F,M,A,M,J,J..... ...,A,S,O,N,D
31,28,31,30,31,...
31,28,31,30,31,... ...30,31,31,.. Lengths of months in days
2,2,4,4,2,6,6,2,8,...
2,2,4,4,2,6,6,2,8,... ...8,2,10,... Table of two
5,4,2,9,8,6,...
5,4,2,9,8,6,... ...7,3,1 Alphabetic Order In Spanish
2,10,12,16,17,18,19,200...
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...
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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