Some consecutive natural numbers, starting with 1, are written on the board. Now, one of the numbers was erased and the average of the remaining numbers is 800/39. Find the number which was erased.

• We know that average of n consecutive numbers average = (n×(n+1)/2)/n = (n+1)/2
  
  If the given n is sufficiently large, the average does not change much even though we exclude one or two numbers from it. So the approximate number of observations is almost double to the average (Remember: the average of consecutive numbers almost lies in the middle)
  The approximate average is 800/39 = Approx 20. So the initial numbers may be nearer to 40.
  In this question it is actually 40 as from the denominator of the new average 800/39. The initial numbers are 40.
  
  Sum of 40 consecutive numbers = 40×(40+1)/2 = 820
  
  Sum of 39 numbers = average x number of observations = 800/39 × 39 = 800
  So the number excluded = 820 - 800 = 20
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