Question

The first five terms of an arithmetic sequence are 8, 13/2, 5, 7/2, and 2. Which function, f(x), could be used to describe the xth term of the sequence?

f(x)=?

Answer 1

The nth term of the sequence is:

`a_n=(-3n+3)/(2)+8`

Explanation:

Given the first 5 terms of the arithmetic sequence

8, 13/2, 5, 7/2, and 2

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

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

as the common difference 'd' is:

`d=a_(n+1)-a_n`

Computing the differences of all the terms

`(13)/(2)-8=-(3)/(2),\:\quad \:5-(13)/(2)=-(3)/(2),\:\quad (7)/(2)-5=-(3)/(2),\:\quad \:2-(7)/(2)=-(3)/(2)`

`d=-(3)/(2)`

The first element is:

`a_1=8`

Therefore, the nth term is computed by:

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

`a_n=-(3)/(2)\left(n-1\right)+8`

`a_n=(-3n+3)/(2)+8`

Therefore, nth term of the sequence is:

`a_n=(-3n+3)/(2)+8`