Question 1102910
<pre>
{{{f(n)=f(n-1)-1/2}}}

{{{f(n)-f(n-1) = -1/2}}}

The left side is the difference between one term
and the preceding term.

So this is an arithmetic sequence with
common difference = {{{d=-1/2}}} and first term {{{a[1]=f[1]=8&1/2}}}

{{{a[n]=a[1]+(n-1)d}}}

{{{f[n]=8&1/2+(n-1)(-1/2)}}}

{{{f[n]=17/2-expr(1/2)(n-1)}}}

{{{f[n]=17/2-expr(1/2)n+1/2}}}

{{{f[n]=18/2-expr(1/2)n}}}

{{{f[n]=9-expr(1/2)n}}}   <-- explicit rule

Edwin</pre>