Area of squares formed by joining midpoints repeatedly in C?

Area of a square is equal to the product of sides of the square.

We are considering a figure in which the midpoints of sides of each square make another square. And so on until a specific number of squares.

This figure shows a square made by joining the midpoints of a square.

For this figure the let the side be a,

The length of side of inner square will be

L2 = (a/2)2 + (a/2)2
L2 = a2(1/4 + 1/4) = a2(1/2) = a2/2
L = a2/ (\sqrt{2}).

Area of square2 = L2 = a²/2.

For the next square, the area of square 3 = a²/4

Lets take an example, tge

Now are we can infer from here about areas of consecutive squares,

a², a²/2, a²/4, a²/8, …..

This is a GP with a² being the first term of the and ½ being the common ratio.

Example

#include <stdio.h>
#include <math.h>
int main() {
   double L = 2, n = 10;
   double firstTerm = L * L;
   double ratio = 1 / 2.0;
   double are = firstTerm * (pow(ratio, 10)) ;
   printf("The area of %lfth square is %lf", n , sum);
   return 0;
}

Output

The area of 10th square is 0.003906