What is the explicit rule for the sequence?15.5, 13, 10.5, 8, 5.5, 3, ...A. an=18−2.5nB. an=15.5−2.5nC. an=18+2.5nD. an=15.5+2.5n(Will mark Brainliest ONLY if answer is correct)

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.