Question
Which arithmetic sequence is described by the linear function f(n) = 1/2n − 13?
Answers
GPT 3.5
The arithmetic sequence described by the linear function f(n) = 1/2n − 13 is 13, 13.5, 14, 14.5, 15, ...
haechan
Which arithmetic sequence is described by the linear function f(n)=1/2n−13?
show all work and write them as simplified fractions
show all work and write them as simplified fractions
GPT 3.5
To find the arithmetic sequence described by the linear function f(n) = 1/2n − 13, we first need to rewrite the given equation in a general form for an arithmetic sequence.
The general form for an arithmetic sequence is given by An = a + (n - 1)d, where:
- An is the nth term of the sequence,
- a is the first term of the sequence,
- n is the term number, and
- d is the common difference between terms.
Given f(n) = 1/2n - 13, we need to rewrite this in the form of An = a + (n - 1)d.
f(n) = 1/2n - 13
f(n) = (1/2)n - 13
f(n) = (1/2) + (1/2)(n - 1) [Rewriting in the form of An = a + (n - 1)d]
f(n) = 1/2 + 1/2n - 1/2
f(n) = 1 + 1/2n - 1
f(n) = 1/2n
From the equation above, we can determine:
a = 1
d = 1/2
Therefore, the arithmetic sequence described by the linear function f(n) = 1/2n − 13 is:
1, 1.5, 2, 2.5, 3, ...
The general form for an arithmetic sequence is given by An = a + (n - 1)d, where:
- An is the nth term of the sequence,
- a is the first term of the sequence,
- n is the term number, and
- d is the common difference between terms.
Given f(n) = 1/2n - 13, we need to rewrite this in the form of An = a + (n - 1)d.
f(n) = 1/2n - 13
f(n) = (1/2)n - 13
f(n) = (1/2) + (1/2)(n - 1) [Rewriting in the form of An = a + (n - 1)d]
f(n) = 1/2 + 1/2n - 1/2
f(n) = 1 + 1/2n - 1
f(n) = 1/2n
From the equation above, we can determine:
a = 1
d = 1/2
Therefore, the arithmetic sequence described by the linear function f(n) = 1/2n − 13 is:
1, 1.5, 2, 2.5, 3, ...