I have opened the image you provided. It presents a pattern recognition problem where you're asked to complete the sequences.

Let's break down each part:

1. Part (a): The shapes start with a triangle, followed by a square, then a pentagon. The next shapes would logically follow polygons with 6 sides (hexagon), 7 sides (heptagon), and 8 sides (octagon).

2. Part (b): A single circle, followed by a pair of two circles, and then a triangle arrangement of three circles. The next pattern would be four circles in a square, then five circles forming a pentagon, and finally six circles forming a hexagon.

3. Part (c): The first shape is a large square. The second divides it into two vertical sections, and the third divides it into four sections. The next divisions should split the square into 8, then 16, and finally 32 sections.

4. Part (d): A single circle, then three circles in a triangular formation, and six circles in a larger triangle. The next step should involve 10 circles, 15 circles, and finally 21 circles arranged in increasingly larger triangular patterns.

5. Part (e): The first pattern shows one vertical line. The second shows an "E" shape with three horizontal lines. The third pattern adds another vertical line to form an "H" shape. The next steps would likely form shapes with more vertical and horizontal lines, expanding on this structure.

If you'd like, I can generate an illustration completing these patterns based on this analysis. Would you like that?

Also, here are some relative questions and tips:

1. How can you predict the next shape in a sequence of polygons?
2. What is the general pattern in increasing the number of circles in geometric formations?
3. How does symmetry play a role in shape and number patterns?
4. Why do some patterns involve both shape changes and numerical progressions?
5. What could be other applications of such patterns in real-life situations?

Tip: When recognizing patterns, always look for changes in the number of sides, objects, or divisions, as they often form the basis for the next terms.