The question is asking for the general term of an arithmetic sequence where the first term $a_1 = 8$ and the second term $a_2 = 16$.

Step 1: Finding the common difference ($d$)

In an arithmetic sequence, the common difference $d$ is calculated as: $d = a_2 - a_1 = 16 - 8 = 8$ So, the common difference is $d = 8$.

Step 2: General formula for an arithmetic sequence

The general term of an arithmetic sequence is given by: $a_n = a_1 + (n - 1)d$ Substituting $a_1 = 8$ and $d = 8$: $a_n = 8 + (n - 1) \cdot 8 = 8 + 8n - 8 = 8n$

Thus, the correct expression for the general term of the sequence is: $a_n = 8n$

Looking at the answer choices:

• $\text{A: } 4n - 2$
• $\text{B: } 2n + 4$
• $\text{C: } 2n + 2$
• $\text{D: } 4n + 2$

None of these options exactly match $a_n = 8n$, so there seems to be an error in the provided choices. However, based on the sequence structure, the correct general term is $8n$.

Would you like any further clarification or assistance?

Related Questions:

1. How do you find the general term for a geometric sequence?
2. What is the formula for the sum of an arithmetic series?
3. How can you verify the common difference in an arithmetic sequence?
4. What are some key differences between arithmetic and geometric sequences?
5. How would the formula change if the first term were different?

Tip: Always confirm the common difference by checking several terms in the sequence.