Answer:
Option: C is the correct answer.
C. [tex]a_n=a_{n-1}-3\ ;\ a_1=2[/tex]
Step-by-step explanation:
The sequence is given by the explicit formula as:
[tex]a_n=5-3n[/tex]
where [tex]a_n[/tex] is the nth term of the sequence.
Also, the first term of the sequence is: [tex]a_1[/tex]
i.e.
[tex]a_1=5-3\times 1\\\\i.e.\\\\a_1=5-3\\\\i.e.\\\\a_1=2[/tex]
Also,
[tex]a_n=5-3n\\\\i.e.\\\\a_n=5-3n+3-3\\\\i.e.\\\\a_n=5-3(n-1)-3\\\\i.e.\\\\a_n=a_{n-1}-3[/tex]
Hence, the recursive formula which represents the same sequence is:
Option: C
