Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

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Solution

Let the height, slant height, lateral edge and base edge of the square pyramid be h units, l units, e units and b units respectively.

We know that

Thus, we have the sequence as h², l², e² =

Now,

Since the common difference is same, the terms h², l², e² form an arithmetic sequence.

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Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

Let the height, slant height, lateral edge and base edge of the square pyramid be h units, l units, e units and b units respectively. We know that Thus, we have the sequence as h2, l2, e2 = Now, Since the common difference is same, the terms h2, l2, e2 form an arithmetic sequence.

Let the height, slant height, lateral edge and base edge of the square pyramid be h units, l units, e units and b units respectively.

We know that

Thus, we have the sequence as h², l², e² =

Now,

Since the common difference is same, the terms h², l², e² form an arithmetic sequence.