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 term
n is the number of terms and
d 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]
