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My first question ever, and my last question yet.


Alec and Beau race to compute 1 + 2 + 3 + ... + n. Alec skips two numbers and gets a sum of 92. Beau double-counts two numbers and gets a sum of 145. What is the value of n?

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mhanifa

Answer:

  • n = {14, 15, 16}

Step-by-step explanation:

This is a sum of the first n terms of an AP:

  • S = (1 + n)*n/2

The true sum is between 92 and 145:

  • 92 < n(n + 1)/2 < 145
  • 184 < n(n + 1) < 290
  • 184 < n² + n < 290
  • 185 < (n + 1/2)² < 291
  • √185 < n + 1/2 < √291
  • 14 ≤ n < 17

Let n = 14

  • S = 14*15/2 = 105

Let n = 15

  • S = 15*16/2 = 120

Let n = 16

  • S = 16*17/2 = 136

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