Question

The sum of the squares of three consecutive natural numbers is 2030.What is the middle number?

• A. 25
• B. 26
• C. 27
• D. 28
• E. 24

Answer 1

The correct option is B

26

Let the numbers be x and x+1 and x+2

Then, $x^2+{\left(x+1\right)}^2+{\left(x+2\right)}^2=2030\iff 3x^2+6x-2025=0.$ $\iff x^2+2x-675=0\iff \left(x+27\right)\left(x-25\right)=0\iff x=25.$

$\therefore$ Middle number = $\left(x+1\right)=26.$