Question

Holiday Homework - Apeejay School
Class IV~VI

Find four ways to make a sum of 45 with consecutive numbers.

2 numbers : ________ + _______ = 45
3 numbers : ________ + _______ + _______ = 45
4 numbers : _______ + _______ + _______ + _______ = 45
5 numbers : _______ + _______ + _______ + _______ + ______ = 45

Answer 1

2 numbers : _22___ + ___23____ = 45 3 numbers : ___14_ + ___15__ + __16_____ = 45 4 numbers : ____7__ + ___8_ + __9___ + _10__ = 45 5 numbers : _____7__ + ____8___ + ____9___ + ______10_ + ____11__ = 45

Answer 2

n + n+1  = 45    =>  n = (45-1)/2 = 22    hence, 
   22 + 23 = 45
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n + n+1 +  n+2 = 45  =>  3 n + 3 = 45    =>    n = 14
   14 + 15 + 16 = 45
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n + n+1 + n+2  + n+3 = 4 n + 6 = 45      =>  n = 39/4
   So  n is not an integer.   It is not possible to express 45 as a sum of 4 consecutive integers.  But with real numbers with a difference of 1, possible.
   9.75 + 10.75 + 11.75 + 12.75 = 45
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 n  +  n+1 + n+2  + n+3  + n+4  = 5n+10 = 45
     n = 35/5 = 7
  7 + 8 + 9 + 10 + 11 = 45
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6 consecutive numbers :
   n + n+1 + n+2  + n+3  + n+4 + n+5 =  6 n + 15  = 45
         n = 5
  5 + 6 + 7 + 8 + 9 + 10 = 45