A sequence is a collection of objects that are arranged in a given order
The sequence of the area of the strip of paper are as follows;
A. The sequence is a geometric sequence
B. The recursive rule for the sequence is f(n) = (1/3) × f(n - 1)
C. The type of "n" value that will wok for the sequence are 0 ≤ n ≤ 5
D. The type of "n" values that will not work are "n" values that are negative
The reason the above values are correct is as follows:
The known parameter are;
The initial area of the piece of paper, A = 81 cm
The area that is cut off from the strip, A₁ = (1/3) × A
The further are cut off, A₂ = (1/3) × A₁
A. Required:
Indicate the type of sequence in the question, geometric or arithmetic
Solution:
The sequence is a geometric sequence given that each are is (1/3) multiplied by the previous area
The common ratio is (1/3)
Geometric sequence
B. Required:
To write the recursive rule of the sequence, including the functions f(n) and f(n - 1)
Solution:
The recursive rule for the sequence is f(n) = (1/3) × f(n - 1)
C. Required:
The type of "n" value that will for the sequence
Solution:
From the graph, for whole number values of f(n), the type of "n" value that will wok for the sequence is 0 ≤ n ≤ 5, which is the domain of the graph
Generally, for a geometric sequence, the possible n values are 0 ≤ n ≤ ∞
D. Required:
To state the type of "n" values that will not work for the sequence
Solution:
The type of "n" values that will not work for the sequence is negative "n" values, because the range of the graph is 0 to 85, with f(0) = 81, such that f (-1) = 243, which is outside the graph area
Learn more about geometric sequence here:
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