Squares that are 1 unit by 1 unit&nbsp;Predicts the perimeter of the 20th figure&nbsp;

Question

Squares that are 1 unit by 1 unit&amp;nbsp;Predicts the perimeter of the 20th figure&amp;nbsp;

fudzisako · Accepted Answer

To solve the problem, we need to find the perimeter of the 20th figure.
Let's consider the pattern: Each figure consists of a square with sides measuring 1 unit. As we progress, we add smaller squares along the perimeter of the previous figure, with each new side having a length of 1 unit.
To find the perimeter of the 20th figure, we need to calculate the total length of all the sides.
Let's denote the perimeter of the nth figure as

P_{n}

.

P_{1}

is the perimeter of the first figure, which is simply the length of its four sides, each measuring 1 unit:

P_{1} = 1 + 1 + 1 + 1 = 4

units.
For each subsequent figure, we add 4 more sides of length 1 unit to the previous figure's perimeter. Therefore, we can express the perimeter of the nth figure recursively as: