Jun 8, 2012

Number System : 110 Sum of 9 Consecutive Numbers

What is the Sum of all the numbers Less then 100, that can be written as the Sum of 9 Consecutive Integers. Where the Sum of 9 Consecutive Integers should be 100. 


Soln : 

0= -4+ -3+..   +0+  ..+3+4


9=  -3+ -2+....+5


18= -2+-1+....+6


27=-1+ 0+......+7


36= 0+1+.......+8


45= 1+2+........+9
....
....
99= 7+8+........+15

so, answer is =
0+9+18+27+36+45+54+63+72+81+90+99  = 9(1+2+3+4+5+6+7+8+9+10+11) =9* (11*12/2) =9* 11*6 
=594   


Note : All numbers which are less less than 100  are considered  as whole numbers

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