93.7k views
2 votes
The sum of the first 8 term of arithmetic sequence is 104 and the sum of the next 12 term is 636, then find, what is common difference, what is generally term

1 Answer

2 votes

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.

User Gabriele Mariotti
by
7.6k points