An arithmetic sequence begins

Find the first term in the sequence which is smaller than $-1000.$

You need to work towards finding an expression for the $n^{\text{th}}$ term, and to do that we need to find $k.$

In an arithmetic sequence, the difference between the first and second term is equal to the difference between the second and third term...

... so $u_2-u_1=u_3-u_2$ ...

... so $15-3k=-k-15$