Jun 7, 2012

Number System : 9 Consecutive Integers

Number System 

What is the Sum of all the numbers Less then 100, that can be written AS the Sum of 9 Consecutive Integers. ( Sum of 9 Consecutive integer shud be less than 100)

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   (here all no.s .which r less than 100  r considered  whole no.s)

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