5. TBQ-Graphical Representation of GP

A school display displays a model made using colored beads. The number of beads used in the model increases in a pattern. The first arrangement uses \(5\) beads, the second uses \(15\) beads, the third uses \(45\) beads, the fourth uses \(135\) beads, and the fifth uses \(405\) beads. How can this pattern be represented graphically?

 

1. Determine the explicit formula for the $n$th term

 

2. Identify the type of curve represented by the pattern