Answer:
[tex]a_n=4-n[/tex]
Step-by-step explanation:
Recall the definition of the general nth term of an arithmetic sequence of common difference "d":
[tex]a_n=a_1+(n-1)\,d[/tex]
we can use this formula to find the common difference knowing the first and fourth terms, and then write the general form for the sequence:
[tex]a_n=a_1+(n-1)\,d\\0=3+(4-1)\,d\\0=3+3\,d\\0-3=3\,d\\d=-1[/tex]
Then the general form for the nth term of this sequence is:
[tex]a_n=3+(n-1)\,(-1)\\a_n=4-n[/tex]
