Answer:
The arithmetic sequence is: 3, -1, -5, -9, -13
Step-by-step explanation:
Recall that the nth term of an arithmetic sequence is defined via the formula:
[tex]a_n=a_1+(n-1)\,d[/tex]
where d is the common difference, n is the term number, and [tex]a_1[/tex] is the first term.
Since we know what the first and fifth terms are (3 and -13 respectively), we can find the common difference and with it any of the missing terms:
[tex]a_n=a_1+(n-1)*d\\a_5=a_1+(5-1)*d\\-13=3+(4)*d\\-16=4*d\\d=-\frac{16}{4} \\d=-4[/tex]
now that we know d=-4, we can find the missing terms:
[tex]a_2=3+(2-1)*(-4) = -1\\a_3=3+(3-1)*(-4)= -5\\a_4=3+(4-1)*(-4)=-9[/tex]
