Question

The sum of the squares of any five consecutive numbers is 1455

Answer 1

Let the numbers be n, n+1,n+2,n+3,n+4

n²+(n+1)²+(n+2)²+(n+3)²+(n+4)²=1455

n²+n²+1+2n+n²+4+4n+n²+9+6n+n²+16+8n=1455

5n²+20n+30=1455

5n²+20n=1455-30=1425

5n²=1425-20n

5n=1425-20=1405

5n=1405

n=1405/5

n=281

5 consecutive numbers are 281,282,283,284,285

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