Final answer:
The common difference is 10 and the general term is a_n = 13 + 10(n - 1).
Step-by-step explanation:
To find the common difference and the general term of the arithmetic sequence, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(2a + (n - 1)d)
Where Sum is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
From the given information, we have:
Sum of the first 8 terms = 104
Sum of the next 12 terms = 636
Substituting these values into the formula, we get:
(8/2)(2a + 7d) = 104
(12/2)(2a + 11d) = 636
Simplifying the equations, we have:
4a + 14d = 104
6a + 33d = 636
Now we can solve these equations simultaneously to find the values of a and d. Solving the equations, we find that a = 13 and d = 10.
Therefore, the common difference is 10 and the general term of the arithmetic sequence is an = 13 + 10(n - 1).