ANSWER
The explicit rule for the sequence is
[tex]a_n=18+2.5n[/tex]
EXPLANATION
The terms of the sequence are
[tex]15.5,13,10.5,8,5.5,3,...[/tex]
The first term of the sequence is
[tex]a = 15.5[/tex]
and the constant difference is
[tex]d =13 - 15.5 = - 2.5[/tex]
Since there is a constant difference, it means the sequence is an arithmetic progression.
The general formula for an arithmetic sequence is given by the formula,
[tex]a_n=a+(n-1)d[/tex]
We substitute the above values to obtain,
[tex]a_n=15.5 - 2.5(n-1)[/tex]
We expand to obtain,
[tex]a_n=15.5 - 2.5n + 2.5[/tex]
This will simplify to,
[tex]a_n=18+2.5n[/tex]
Therefore the correct answer is A.
