If the sum of 4 consecutive numbers is 10, what is the sum of their squares?  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The sum of 4 consecutive numbers is 10. Let the smallest of the 4 numbers be x. So the numbers are x, x+1, x+2 and x+3. Adding them we get 4x+6. Equating 4x + 6 to 10 we get 4x + 6 = 10

=> 4x = 10-6

=> 4x = 4

=> x = 1

So the four numbers are 1, 2, 3 and 4.

Now the squares of 1, 2, 3 and 4 are 1, 4, 9 and 16. The sum of 1, 4, 9 and 16 is 1 + 4 + 9 + 16 = 30.

Therefore the sum of the squares of four consecutive numbers that have a sum of 10 is 30.

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neela | High School Teacher | (Level 3) Valedictorian

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The sum of the 4 consecutive numbers is 10.

If the first number is x, then the other 3 numbers are x+1,x+2 and x+3.

Therefore their sum = x+(x+1)+(x+2)+(x+3) = 10.

Therefore, 4x+6 = 10.

Therfore 4x = 10-6 = 4.

4x= 4

x = 4/4 = 1.

Therefore the consecutive numbers are 1,2,3 and 4.

So the sum of the squares of the 4 consecutive numbers= 1^2+2^2+3^2+4^2 = 1+4+9+16 = 30.

Therefore the sum of the squares of these 4 consecutive numbers = 30.

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