Don't fall in

Algebra Level 1

A sinkhole begins to open up in a deserted country. In the first year, the sinkhole is a 1 m1\text{ m} square, and every year afterwards it grows an additional 1 m1\text{ m} square from each of its outer edges.

Steve notices the following pattern with the sinkhole area: 02+12=112+22=522+32=1332+42=25.\begin{aligned} 0^2+1^2 &= 1 \\ 1^2+2^2 &= 5 \\ 2^2+3^2 &= 13 \\ 3^2+4^2 &= 25. \end{aligned} Is the sinkhole area always the sum of the squares of two consecutive integers?

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