Respuesta :
Answer:
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.
In the fifth generation 1024 people learnt the art of quilling.
What is a geometric series?
- A geometric series is a series for which the ratio of each two consecutive terms is a constant and called the common ratio.
- Nth term of the Geometric series is given as [tex]t_{n} = ar^{n-1}[/tex] where a is the first term of the series and r is the common ratio.
How to find how many people will know the art of quilling?
- In the first generation , 4 people learnt the art of quilling.
- In second generation (4 x 4) = 16 people learnt the art of quilling.
- In the third generation (16 x 4) = 64 people learnt the art of quilling.
- In the fourth generation (64 x 4) = 256 people learnt the art of quilling.
- In the fifth generation ( 256 x 4) = 1025 people learnt the art of quilling.
In the fifth generation 1024 people learnt the art of quilling.
- The series is going as a geometric pattern.
In total 5 generations total (16+ 64 + 256 + 1024) = 1364 people learnt the art of quilling.
Find more about "Geometric series" here: brainly.com/question/24643676
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