Question

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, how many people will know the art of quilling.

Answer 1

Answer:

1024

Step-by-step explanation:

The problem simulates a geometric sequence, where the initial term is 4, its reason is 4 and the last term is at the fifth position. A geometric sequence is defined as

$a_{n}=a_{1}r^{n-1}$

Where:

$n=5\\a_{1}=4\\ r=4$

Replacing these values, we have

$a_{n}=a_{1}r^{n-1}\\a_{5}=4(4)^{5-1}=4(4)^{4} = 1024$

Therefore, after 5 generations, 1024 people will know the art of quilling.

It's important to know why this is a geometric sequence.

Geometric sequences are built by multiplying a factor to an initial value to obtain a second term, then this second term is multiplied by the factor to obtain a third term, and so on. Consider that the problem represents this behaviours, because each 4 students will teach 4 more, so the total number multiplies.

Answer 2

1 * 4 = 4

4 * 4 (or $4^{2}$) = 16

16 * 4 *4 *4 *4 *4

16384 people will know the art of quilling