Question

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?

Answer 1

• n = {14, 15, 16}

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