Which arithmetic sequence is described by the linear function f(n) = 1/2n − 13?

Answer 1

The arithmetic sequence described by the linear function f(n) = 1/2n − 13 is 13, 13.5, 14, 14.5, 15, ...

Answer 2

Which arithmetic sequence is described by the linear function f(n)=1/2n−13?

show all work and write them as simplified fractions

Answer 3

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, ...