(Originais Teachy 2024) - Question Medium of Arts

Dance, as a form of artistic expression, reflects not only the culture of a people, but can also incorporate elements from other disciplines, such as mathematics. For example, traditional dances often follow rhythmic and geometric patterns, which can be described by numerical sequences and geometric figures. Consider a folk dance that uses a circular choreographic pattern, where the dancers, during a sequence, move along a circle of constant radius. The choreography begins with a dancer at a fixed point in the center of the circle and the others equally spaced around the circumference. As the dance progresses, each dancer moves while maintaining a constant distance from the previous dancer, thus forming a new inner circle. If the radius of the initial circle is 6 meters and the choreography establishes that the distance between the dancers in each subsequent circle should decrease by 2 meters, determine the number of dancers present in the fifth circle formed. Additionally, analyze how the progression of the dance can be interpreted as a mathematical sequence and identify what the general term of this sequence is.