12. TBQ - Expression for folded rope

Imagine a straight rope. If it is cut once as shown in the picture, we get \(2\) pieces. If the rope is folded once and then cut as shown, we get \(3\) pieces.

 

   

 

Observe the pattern and determine the number of pieces if the rope is folded 21 times and cut: 23 pieces22 pieces19 pieces20 pieces 

 

Find the expression for the number of pieces when the rope is folded r times and cut? r-2r+1r-1r+2