Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

An arithmetic sequence takes the form



where is the common difference between terms. You can solve for in terms of any of the previous terms of the sequence:



for some integer

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term



Given that the 4th term is and the 11th term is , you have the following system of equations.



Solving this system for the two unknowns yields and .

So, the sequence is given explicitly by