Question

Which function describes the arithmetic sequence shown?

The sequence is : -1, 1, 3, 5, 7, 9, 11, 13

Answer 1

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

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.