Given the function f(x) = -5|x + 1 + 3, for what values of x is f(x) = -12?
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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
where
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
Solving this system for the two unknowns yields
So, the sequence is given explicitly by