A recursive rule for an arithmetic sequence is a1=4;an=an−1−3 . What is the explicit rule for this sequence? Enter your answer in the box. an=

Answer:The explicit rule for the arithmetic sequence is given by:[tex]a_n = a_1+(n-1)d[/tex]       ......[1]where,[tex]a_1[/tex] is the first termn is the number of terms andd is the common difference for two consecutive terms.As per the statement:A recursive rule for an arithmetic sequence is:[tex]a_1 = 4[/tex][tex]a_n = a_{n-1}-3[/tex]The recursive formula for the arithmetic sequence is given by:[tex]a_n = a_{n-1}+d[/tex]then;On comparing we get;d = -3 Substitute the given values in [1] we have;[tex]a_n = 4+(n-1)(-3)[/tex]⇒[tex]a_n = 4 -3n+3 = 7-3n[/tex]Therefore, the explicit rule for this sequence is, [tex]a_n = 7 -3n[/tex]