Answer:
Arithmetic sequence
[tex]a_n=\frac{1}{2}-n[/tex] for [tex]n\geq 1[/tex]
Step-by-step explanation:
We are given that a sequence
[tex]-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},-\frac{7}{2},...[/tex]
We have to identify the sequence as arithmetic or geometric and write an explicit formula .
[tex]a_1=-\frac{1}{2}[/tex]
[tex]a_2=-\frac{3}{2}[/tex]
[tex]a_3=-\frac{5}{2}[/tex]
[tex]a_4=-\frac{7}{2}[/tex]
[tex]d_1=a_2-a_1=\frac{-3}{2}+\frac{1}{2}=-1[/tex]
[tex]d_2=a_3-a_2=-\frac{5}{2}+\frac{3}{2}=-1[/tex]
[tex]d_1=d_2=-1[/tex]
When the difference of consecutive terms is constant then the sequence is an arithmetic.
Hence, the sequence is an arithmetic.
[tex]a_n=a+(n-1)d[/tex]
[tex]a_n=-\frac{1}{2}+(n-1)(-1)=-\frac{1}{2}-n+1=\frac{1}{2}-n[/tex] for [tex]n\geq 1[/tex]
