## Perimeter Sequence

#### Problem

The first three stages of a sequence are shown.

What is the perimeter of the tenth in the sequence?

#### Solution

By considering the next in the sequence.

It should be clear that the `n` th in the sequence will be `n` units tall and n units wide, so there will be 2`n` horizontal units and 2`n` vertical units, making the total perimeter 4`n`. That is, the perimeter of the tenth in the sequence will be 40 units.

Problem ID: 76 (May 2002) Difficulty: 1 Star