Respuesta :
Answer:
10,935
Step-by-step explanation:
lvl 1: 15 x 3=45
lvl 2: 45 x 3=135
lvl 3: 135 x 3=405
lvl 4: 405 x 3=1215
lvl 5: 1215 x 3=3645
finally lvl 6: 3645 x 3=10,935
Taylor will earn 3645 points when she completes level 6, using the geometric progression formed from the given information.
What is a geometric progression?
A geometric progression is a series in which every number is the product of the previous number and a common ratio.
The first term of a geometric progression is represented as a.
The common ratio is represented by r.
The n-th term of a geometric progression (aₙ) is determined by the formula,
aₙ = arⁿ⁻¹.
How do we solve the given question?
We are given that Taylor is playing a video game. She earns 15 points when she completes Level 1. Each time she completes a level, she earns three times as many points as the previous level.
We are asked to find the points she will earn when she completes level 6.
The given case can be seen as a geometric progression as the points collected after completion of every level are the product of the previous level's point and a common ratio of 3.
In this geometric progression, a = 15, and r = 3.
We need to find the point collected by Taylor when she completes level 6.
This is the 6th term of our geometric progression. We determine the 6th term using the formula of the n-th term of a geometric progression:
aₙ = arⁿ⁻¹.
∴ a₆ = (15)*(3)⁶⁻¹ = 15*3⁵ = 15*243 = 3645.
∴ Taylor will earn 3645 points when she completes level 6, using the geometric progression formed from the given information.
Learn more about a geometric progression at
https://brainly.com/question/12006112
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