Amanda teaches the art of quilling to four students these students each teach the art of quilling to four other students if this process continues for five generations blank people will know the art of quilling

341

Step-by-step explanation:

The number of people who know the art of quilting in each successive generation is

1, 4, 16, …

These numbers represent a geometric sequence where each term has the form

aₙ = a₁rⁿ⁻¹

In your sequence, a₁ = 1 and r = 4.

Then, the formula for your sequence is

aₙ = 4ⁿ⁻¹

Sum over five generations

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[(1 - rⁿ)/(1 - r)]

Sum = 1[(1 - 4⁵)/(1 - 4)

       = (1 - 1024)/(-3)

       = -1023/-3

       = 341

If the process continues for five generations, 341 people will know the art of quilting.

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