Final answer:
The common difference of the arithmetic sequence is 4 and the general term can be expressed as a_n = 2 + 4(n-1), where n is the term number.
Step-by-step explanation:
To find the common difference and general term of an arithmetic sequence, we need to use the formulas that relate them to the sum of the sequence.
Let's denote the first term of the sequence as a and the common difference as d.
The sum of the first 8 terms can be expressed as:
Sum1 = (8/2) * [2a + (8-1)d] = 104
Simplifying this equation, we get:
16a + 28d = 104
We are also given that the sum of the next 12 terms is 636:
Sum2 = (12/2) * [2(a + 8d) + (12-1)d] = 636
Simplifying this equation, we get:
24a + 156d = 636
We now have a system of two equations:
16a + 28d = 104
24a + 156d = 636
Solving this system of equations, we find that a = 2 and d = 4.
Therefore, the common difference of the arithmetic sequence is 4, and the general term of the sequence can be expressed as an = 2 + 4(n-1), where n is the term number.