We know that, in general, the formula for the \(n\)-th term of an arithmetic sequence with first term \(c_1\) and common difference \(d\) is \(c_n = c_1 + ( n - 1 )d\).
So \(c_3 = c_1 + 2 d = 8\) and \(c_9 = c_1 + 8 d = 56\).
This gives us two equations in the two unknown quantities \(c_1\) and \(d\).
Subtracting the first equation from the second gives \(6d = 48\), so the common difference is \(8\). Substituting \(d = 8\) into the first equation and solving tells us that the first term \(c_1\) equals \(-8\).