Answer
$a_n=\dfrac{111-13n}{5}$
Work Step by Step
We know that the general formula of an arithmetic sequence is given by
$a_n= a_1+(n-1) d$ ...(1)
Here, we have $a_7=a+7b=4$ ..(2)
$a_{12}=a+12b=-9$ ..(3)
Now, we will have to subtract equation (2) from (3).
$5b =-13 \implies b=\dfrac{-13}{5}$
Equation (2) gives: $a_7=a+7(\dfrac{-13}{5})=4$
$a=\dfrac{111}{5}$
Thus, we find that the nth term is: $a_n=\dfrac{111-13n}{5}$
