Answer:
[tex]a_{n}=(-3n + 7)[/tex] is the answer.
Step-by-step explanation:
Here the recursive rule for an arithmetic sequence is
a1 = 4
[tex]a_{n}=a_{n-1}-3[/tex]
Therefore the sequence will be
4, 1, -2, -5........ n terms
For this arithmetic sequence the explicit rule will be
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Here n = number of terms
a1 = first term = 4
d = common difference = -3
[tex]a_{n}=4+(n-1)(-3)= 4 - 3(n-1) = 4 - 3n + 3 = (7 - 3n)[/tex]
Therefore explicit rule for this sequence is [tex]a_{n}=(-3n + 7)[/tex]
