Question

Which function describes the arithmetic sequence shown?

Answer 1

Answer:

The function $a_n=2n-3$ describes the arithmetic sequence.

Step-by-step explanation:

Given the sequence

-1, 1, 3, 5, 7, 9, 11, 13

An arithmetic sequence has a constant difference 'd' is defined by

$a_n=a_1+\left(n-1\right)d$

Compute the differences between all the adjacent terms:

$1-\left(-1\right)=2,\:\quad \:3-1=2,\:\quad \:5-3=2,\:\quad \:7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2,\:\quad \:13-11=2$

As the difference between all of the adjacent terms is the same and equal to

$d=2$

As the first element is

$a_1=-1$

so the term will be:

$a_n=a_1+\left(n-1\right)d$

$a_n=2\left(n-1\right)-1$

$a_n=2n-3$

So, the function $a_n=2n-3$ describes the arithmetic sequence.