Progressions

The integers 1, 2, ..., 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b - 1 is written. What will be the number left on the board at the end?

  1. 821
  2. 820
  3. 819
  4. 781

Answer

Number left on the board will be the sum of numbers from 1 to 40 subtracted by 39.

S = n/2 * (a+l) = 20 * 41 = 820

Number on the board = 820 - 39 = 781

The correct option is D.