The sum of the squares of 5 consecutive whole numbers is 90. What are the five numbers?

Answer 1

One relatively easy way to do this is to make a list of the first 10 squares:

1 4 9 16 25 36 49 64 81 100

and try to find 5 in a row that total to 90.

10 squared is 100. Too much. That can't be part of the answer.

1 + 4 + 9 + 16 + 25 is 55. Too small.

4 + 9 + 16 + 25 + 36 is 90. So the consecutive whole numbers are 2, 3, 4, 5, 6.

The harder way but more fun way for a math teacher would be to make the middle number n. Then, we can set up an equation:

(n-2)2 + (n-1)2 + n2 + (n+1)2 + (n+2)2 = 90

That expands to n2 - 4n + 4 + n2 -2n + 1 + n2 + n2 + 2n + 1 + n2 +4n + 4 = 90

Simplify to 5n2 + 10 = 90

5n2 = 80

n2 = 16

n = 4. The middle number of the 5 numbers is 4. The full set of consecutive whole numbers is 2, 3, 4, 5, 6.

Doing the problem two ways is a great way to enhance understanding and to check your work.