As you can see in the screenshot, once you plot the points for each rectangle, it becomes easier to see what's happening. In the first transformation, the rectangle is translated or slid. In the next 2 transformations, the rectangle is rotated. In the last transformation, the rectangle is dilated or shrunk. The first rectangle is the only translation.
The wording of this question is a bit confusing... You can't write a sequence in sigma notation, but rather a series or sum. I think the question is asking you to write the sum of the sequence,
which would be
in sigma notation.
To do this, notice that the denominator in each term is a power of 2, starting with and ending with . So in sigma notation, this series is