Question

Find the sum of a finite geometric series.
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. If this process continues for 5 generations,
people will know the art of quilling.

Answer 1

At the end of generation I, there are 4+1=5 people who could quilt.

Assuming Amanda continues to teach, and no one gets taught more than once, then at the end of the second generation, each of the five will have taught 4 others (5*4=20) and added to the original five, that makes 25 people after the second generation.

Continue this way to get the number of people who can quilt after the fifth generation.