Let's analyze the pattern in the given problem.

We can see that the general structure of the terms is:

$2 + 4 \times 1 = 6$ $2 + 4 \times 2 = 10$ $2 + 4 \times 3 = 14$ $2 + 4 \times 4 = 18$ $2 + 4 \times 5 = 22$ $2 + 4 \times 6 = 26$ ...

This shows a consistent pattern where the first term is always 2, the second term is 4, and the variable $n$ (representing the position of the term) is multiplied by 4. The formula seems to be:

$2 + 4 \times n$

Thus, for $n = 20$, the 20th term would be:

$2 + 4 \times 20 = 2 + 80 = 82$

Looking at the options:

• A) $5 + n$ – Incorrect.
• B) $6 + n$ – Incorrect.
• C) $2 + 4 \times n$ – Correct.
• D) $6 + 4 \times n$ – Incorrect.

So, the correct formula is C) $2 + 4 \times n$.

Would you like any further clarifications?

Here are some follow-up questions:

1. What is the formula for the nth term in arithmetic sequences?
2. How do you find the sum of the first n terms in an arithmetic sequence?
3. Can you apply this formula to other similar problems?
4. What happens if the pattern uses different numbers, like 3 and 5 instead of 2 and 4?
5. How would you approach finding the nth term if the pattern involved subtraction instead of multiplication?

Tip: When working with patterns, always look for consistency in how the terms are changing—addition, subtraction, multiplication, etc.