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:

The nth term of the sequence is:

[tex]a_n=\frac{-3n+3}{2}+8[/tex]

Step-by-step 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:

[tex]a_n=a_1+\left(n-1\right)d[/tex]

as the common difference 'd' is:

[tex]d=a_{n+1}-a_n[/tex]

Computing the differences of all the terms

[tex]\frac{13}{2}-8=-\frac{3}{2},\:\quad \:5-\frac{13}{2}=-\frac{3}{2},\:\quad \frac{7}{2}-5=-\frac{3}{2},\:\quad \:2-\frac{7}{2}=-\frac{3}{2}[/tex]

[tex]d=-\frac{3}{2}[/tex]

The first element is:

[tex]a_1=8[/tex]

Therefore, the nth term is computed by:

[tex]a_n=a_1+\left(n-1\right)d[/tex]

[tex]a_n=-\frac{3}{2}\left(n-1\right)+8[/tex]

[tex]a_n=\frac{-3n+3}{2}+8[/tex]

Therefore, nth term of the sequence is:

[tex]a_n=\frac{-3n+3}{2}+8[/tex]

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