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
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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